FCC Media Study No. 9:
A Theoretical Analysis of the Impact of Local Market
Structure on the Range of Viewpoints Supplied
Isabelle Brocas
University of Southern California
and CEPR
Juan D. Carrillo
University of Southern California
and CEPR
Simon Wilkie
University of Southern California
June 2011
Table of Contents
1. Executive Summary ................................................... 2
2. Background ............................................................ 4
3. Literature Review ...................................................... 6
4. Measuring Welfare in Media Markets .................................. 11
5. Model Preliminaries ................................................... 17
6. Model I: Disclosure under the Veil of Ignorance ........................ 18
7. Model II: Disclosure under the Threat of Sabotage ..................... 22
8. Model III: Disclosure, Competition and Reputation Costs .............. 26
9. Experimental Design and Procedures .................................. 29
10. Results of Experiment 1 ............................................... 32
11. Results of Experiment 2 ............................................... 39
12. Concluding Remarks and Future Research ............................. 46
13. References ............................................................. 49
14. Appendix A: Figures .............................................. A1-A8
15. Appendix B: Instructions for All Experiments .................... B1-B25
1
1 Executive Summary
In this study we introduce a model of media market competition to examine the
impact of ownership structure on the performance of the market in terms of infor-
mational efficiency and viewpoint diversity. We adopt the classical mathematical
analysis of David Blackwell’s ‘comparison of experiments,’ to measure the quality
and diversity of information transmitted in the market and how that quality in turn
affects welfare. We argue that Blackwell’s method is the appropriate theoretical
metric to measure ‘the market place for ideas.’
We consider the case of a decision maker (e.g., a voter) who requires information
to help her form an opinion or choose an action (e.g., who to vote for). A media outlet
is a source of such information. More precisely a media outlet observes information
that can inform the decision maker/voter and chooses to transmit a signal, which
could vary in its level of accuracy. We define a media viewpoint, as the media owner
having a preference over the policy outcome that will be influenced by the action
chosen by the decision maker. We say there is diversity of viewpoint if the media
market contains different firms with different viewpoints. In particular, a media firm
with a viewpoint may specialize in collecting and disseminating information from a
set of sources aligned with that viewpoint. We will say that a media market exhibits
bias, if in equilibrium a firm suppresses or does not transmit information that is
detrimental to its viewpoint. We will say that a media market exhibits garbling,
when a firm engages in ‘signal jamming’ or transmits signal that garbles the signal
of another media outlet.
We show that with a small number of independent firms the equilibrium will
exhibit bias and garbling. This causes a welfare loss to consumers seeking infor-
mation. In contrast to the classic Steiner result, with multiple outlets owned by
one firm (monopoly) there will be no diversity of viewpoint. The amount of bias
in equilibrium depends on the cost (or loss of profits) versus the gain from biasing
the decision maker. If the cost of biasing or garbling to a media firm increases then
the amount of bias diminishes and consumer welfare increases. We model this cost
as ‘reputation costs.’ That is, if two media outlets have similar viewpoints, the
one with the greater reputation for being informative will have the greater audi-
ence share, and therefore earn more profits. Under the assumption of ‘Informational
Bertrand Competition’ where the more informative firm captures all the market, we
obtain informational efficiency with four firms in the market. The key observation is
that in order to obtain diversity of viewpoint it is not sufficient to have medias with
different viewpoint: competition among firms with the same viewpoint drives in-
formational efficiency. Thus, informational concerns for diversity and localism may
2
require ownership limits more stringent than would be justified by conventional
anti-trust analysis alone.
We then test the model with experimental treatments in a controlled laboratory
setting. The treatments study the incentives of subjects to bias information, garble
information and develop reputations. We find that our theoretical models do quite
well at predicting behavior. In general, media firms do behave strategically by
biasing and garbling information. Consumers learn that they are doing so and
punish firms that withhold information with a smaller market share. We find that
the market has better information transmission with four firms than with two, and
that there is an additional increase in efficiency when there are six independent
firms rather than four. Again this suggest that the number of independent voices is
a concern when we consider the FCC’s diversity and localism goals.
3
2 Background
The Federal Communications Commission (FCC or Commission) has authority over
the allocation of radio spectrum granted by the 1934 Communications Act. The
FCC’s charge is to ensures that the ownership of a license to use spectrum is held
in the “public interest, convenience and necessity.” The FCC’s definition of public
interest, convenience and necessity includes three elements: competition, diversity,
and localism. The FCC reviews transactions conveying the control of a license to
ensure that such transactions fit in with its goals. Beyond the mere review of mergers
the FCC at the behest of Congress has developed several specific rules that limit
the holding of these licenses by entities in the United States. The rules are generally
referred to as the “media ownership rules”. There are six such rules. These rules
broadly fall into three categories; first national rules limiting national ownership of a
particular class of broadcast license (TV or radio), second local rules restricting the
ownership structure in a local geographic market of a particular class of broadcast
license (TV or radio), and third cross-ownership rules limiting ownership across
different classes of media.
The Communications Act of 1996 was the first major rewrite of the 1934 Commu-
nications Act. The theme of the 1996 Act is that, to the extent possible, regulation
should be replaced by competition. In particular as required by the 1996 Act under
Section 202, the FCC is required to conduct a (now) Quadrennial Review of media
ownership regulations to see “whether any such rules are necessary in the public
interest as the result of competition.” The courts have interpreted this clause as
suggesting that the FCC should review the economic evidence of competition and
the impact of New Media to see if the existing ownership rules are still required or
if they are made redundant because of the scope of the increasing competition. To
assist in deliberations, and meeting the demands placed by the Courts, the 2002
and 2006 reviews included a series of studies. Studies were conducted using both
in-house and contracted resources. This study is designed to aid the FCC in its
deliberations and to be incorporated as part of the 2010 Quadrennial Review.
1
This study aims to contribute to this proceeding by investigating how at the
local level the ownership structure of media market would affect the level of com-
petition and in particular affect the performance of the media market in terms of
serving the interests of the community both in the diversity of viewpoint and the
1
The Commission recently issued its Notice of Inquiry in MB Docket No. 09-182 as part of
the 2010 Quadrennial Review. See http://hraunfoss.fcc.gov/edocs public/attachmatch/FCC-10-
92A1.pdf. See also, 2006 Quadrennial Regulatory Review: Report and Order and Order on Recon-
sideration, available at http://hraunfoss.fcc.gov/edocs public/attachmatch/FCC-07-216A1.pdf.
4
impact on localism. The FCC rules under review include limits on local TV and
radio station ownership, TV-radio cross-ownership, and newspaper-broadcast cross-
ownership. These rules are defined with respect to local markets (e.g., the Nielsen
Designated Market Area, or DMA, and the Arbitron Radio Metro). Because the lo-
cal television, local radio, and cross-ownership rules under consideration are defined
with respect to local markets, this study is focused on local markets as the primary
unit of analysis. This theoretical study is designed to address the Commission’s
diversity and localism goals, thereby supplementing the empirical analysis in other
studies.
The approach assumed in this paper is that the Commission’s goal of competition
is adequately handled by existing economic anti-trust analysis. Indeed, reviews of
any major transaction would be jointly undertaken by both the FCC and either
the Department of Justice or the Federal Trade Commission applying existing anti-
trust laws. This approach would limit the amount of concentration of ownership
in any particular geographic market. Therefore, we do not consider the impact on
traditional economic metrics such as pricing and quantity consumed. We feel that
there is little new to contribute to this existing standing body of anti-trust economics
and law, so we develop a different approach here. The question asked is do the goals
of diversity and localism require a more stringent or different standard in particular
circumstances? We are interested in the questions of how concentration of ownership
in the local geographic level will impact the quality of local information transmitted
and the diversity of viewpoints expressed.
If we examine the scope of national news media, we find that in addition to
the existing licensed FCC entities such as television stations and radio broadcast
stations, there is a plethora of other information sources. In particular, there is the
wide body of newspapers including newspapers that have a national footprint such
as, The New York Times, USA Today and the Wall Street Journal. There is also a
national news print magazines. There are multiple Cable TV News networks such
as CNN and Fox News. In addition, there is of course the burgeoning Internet, the
increasing prevalence of conventional media sources on the web, such as NBC.com,
NewYorkTimes.com and WashingtonPost.com. In addition, the Internet provides
unfiltered access to the AP and Reuters newswire through services such as Google
and Yahoo! This leads us to believe that there is indeed sufficient national coverage
independent of one’s location such that the rules on ownership at the national level
are largely irrelevant. When we turn to coverage of the local market, however, there
seems to be much more relevant concentration and in particular a lack of diversity
of authoritative and reliable news sources at the local level compared with those
that exist at the national level. Therefore, our focus in this study is at the local
5
level where there may be just a few broadcast television and radio stations, and a
dwindling number of print media.
3 Literature Review
We now turn to a brief review of the existing literature on the economics of the
media. In particular, we discuss the extant economic literature and how it relates
to the current study. At the outset, it must be said that the body of literature on
the economics of the media does not approach the volume and depth of coverage
that has been expended on modeling the telecommunications sector. Moreover, the
area of media economics is developing rapidly and much of the most important and
relevant literature is very recent. We include many recent papers in the references
that document or analyze media viewpoint and bias that we do not discuss directly
here.
Early work studying the media goes back to the classic paper by Peter Steiner.
Steiner (1952) adopted the Hotelling model of spatial competition to the case of
media (radio), choosing either what might be thought of as a viewpoint or a pro-
gramming mix or radio format. In Steiner’s radio model one obtains the following
result. If we have a mass of consumers located along a line (which we might think
of as the diversity of viewpoints from left to right or from lowbrow to highbrow tele-
vision) and the distribution is single peaked, then the largest mass audience would
be located at the median. In a broadcast market driven by advertising revenues,
this median preference is where a profit maximizing single firm would locate. If we
now introduce competition through a second firm, where would that firm locate?
The Hotelling paradox is that the entrant would locate right next to the existing
firm. That way, the firm slightly to the left of the median controls all the audience
to the left and the firm slightly to the right controls all the audience to the right.
The equilibrium is such that firms choose the same spatial location and split the
market 50-50. However, entry is detrimental for the first firm as the new firm is now
cannibalizing the market of the existing firm. Therefore, if instead we introduce
the second license and allocate it to the incumbent, the monopolist owner of two
licenses (or duopolist in FCC parlance) would in fact choose to relocate both firms
and spread them out so that they do not cannibalize each other’s market. Therefore,
the Steiner result is that we would have greater diversity with monopoly than we
would under competition. In an empirical paper, Berry and Waldfogel (2001) test
this result by examining the impact of radio mergers on a station’s format choice.
They indeed find support for the result. However, although interesting, the model’s
application is limited to format choice rather than viewpoint. In particular, firms
6
are assumed to have no preference over their choice of location other than market
share. That is, the Steiner model assumes away the possibility that media firms
might want to shape taste or opinion for either future profit or pure preference rea-
sons. Secondly although the model is sensible as a model of format competition, as
we will show it makes less sense once we consider the content ‘information.’ More-
over, the Steiner result is not robust to the introduction of three or more firms as
it becomes very difficult to describe what will be the equilibrium location in the
extended model.
Influential work on the regulation of television has been done in the 1970s and
1980s by economists in the so-called “public choice” framework. In particular,
Besson et al. (1984) investigated the role of the FCC in terms of limiting entry
into the market and also enforcing vertical contracting relations between networks
and their affiliate stations. The authors investigated the relationship between the
networks and programming suppliers, or the so-called “financial syndication rules”.
Although this work is important, it is also of limited relevance to the issues here, as
we do not focus on the vertical issues.
Another area of research, which is relevant to our current study, is a stream
of literature investigating whether or not ownership matters. In particular this is
highly relevant to our analysis. Most of this literature is empirical and it begins with
the classic paper by Dubin and Spitzer (1993) which investigated if the ownership
structure affects the choice of format in radio. In that study, they found that
the race of the owner affected the probability that a station would choose to play
in a minority favored format. In particular, African-American ownership meant
that it was more likely that the station would play an African-American format.
Subsequent to the study, the paper by Siegelman and Waldfogel (2001) replicated
these results. In particular, that study found that the ownership structure not only
affects the format but also the welfare market that minority audiences increase with
minority ownership. Obelholzer, Gee and Waldfogel (2006) argue that the result has
implications for localism. That is, in markets where there are more Spanish language
radio stations there is higher civic participation as measured by voter turnout among
Hispanics.
These findings are consistent with the political science literature that studies the
importance of information in voting behavior. For a detailed treatise on the topic
of how voters use information and how information affects their behavior we refer
to Alvarez (1998). In particular, Alvarez examines several presidential elections and
finds that if voters have less information about a candidate then (controlling for
other factors) they are less likely to vote for that candidate. In addition, he finds
that the amount of media exposure and political information voters have also affect
7
their voting behavior. This informational impact is important given the concern of
‘localism.’ Political scientists have studied the so called “roll-off” phenomenon, that
a voter will go through the cost of turning out to vote but not vote on every issue.
In particular many voters will vote in the Presidential and Senate elections but not
for example the local school board. Considering that their vote is much more likely
to be pivotal in a local rather national or statewide election, to an economist this
behavior is odd. One rationale that is provided is based on the quality of informa-
tion. The national media provides extensive coverage of the Presidential candidates
positions and competence, but there is a shortage of local information about local
elections. Confronted with the lack of quality information people choose to abstain,
see Feddersen and Pesendorfer (1996) as well as Katz and Ghirardato (2002). Thus,
there is a direct linkage between the quality and diversity of information in a local
media market and civic participation, which impacts the FCC’s ‘localism’ concerns.
In this study we show that the quality and diversity of information in turn is linked
to market structure.
There is also a long literature examining media bias that we will not review here
as most of it is beyond our expertise. Recently, there has been a new and sophis-
ticated analysis of measures of media bias or slant using econometric techniques.
In particular, the work by Groseclose and Milyo (2005) provides a careful study
of the viewpoint or bias of different media. Their work and that of the empirical
papers that follow use the Poole-Rosenthal (1997) score a measure of the ideological
locations of all of the politicians who served in the U.S. Congress. They find that
indeed there is a difference of viewpoint and that different media institutions are
well associated with a particular left of center or right of center view. For instance
the New York Times is recognized as being a left of center viewpoint, and the Fox
News Channel is recognized as being a right of center viewpoint. These findings
have also been found in other studies using similar methodologies. Gentzkow and
Shapiro (2010) undertake a textural analysis find evidence of bias and that it is
demand driven, that is newspapers exhibit a bias to because of the prior belief of
the electorate. Puglisi and Snyder (2008) examine the media coverage of political
scandals. They find that even controlling for the local Partisan tastes there is bias
in that a Democrat-leaning paper will spend relatively more space on Republican
scandals than Democrat scandals and Republican-leaning papers do the opposite.
They find that the coverage of local scandals rather than national scandals is more
driven by local electoral bias.
DellaVigna and Kaplan (2006) studies the introduction of the Fox News Channel
on cable television systems. Although Fox News is of course not a broadcast station
and therefore subject to FCC, the experiment is interesting because the rollout of
8
Fox News has the characteristics of a randomized trial. That is, Fox News was
shown on some cable systems where they reached the contractual arrangement and
not on others, in what appears to be a somewhat random fashion because of the
quilt of ownership of cable networks platforms in the United States. Given this ran-
domized “treatment” the authors ask if in the treated markets the voting behavior
is different from similar matched markets that were not treated by the introduction
of Fox News. What DellaVigna and Kaplan find is that indeed there is an impact of
the Fox News introduction resulting in a somewhat higher vote for the Republican
candidates than would be expected. The authors then build a structural model to
examine behaviorally if and by what mechanism Fox News’s introduction changes
the opinion of voters. They find that the dominant effect seems to be that the ex-
posure to the information transmitted by Fox News changed opinions. In a related
experimental study, Gerber, Karlan and Bergan (2009) randomly assigned house-
holds free subscriptions to either the Washington Post or the Washington Times.
They find that the households assigned to the Washington Post were eight percent-
age points more likely to vote for the Democratic candidate for governor than those
assigned to the control group. Thus, we conclude from the empirical literature that
the ownership of media outlets matters viz-a-viz viewpoint, and that the informa-
tional content of a media market can have an effect on how people make decisions
such as choosing whether or not to vote and, when they do, who to vote for. Ander-
son and McLaren (2010) provide several examples of information suppression, and
Enikolopov, Petrova and Zhuravskaya (2011) document the influencing of electoral
outcomes in Russia. Therefore, from the literature, we conclude the FCC has as
a powerful interest in examining the relationship between ownership structure and
market performance, in terms of the efficiency of transmission of information and
the diversity of viewpoints in the market.
There are several recent theoretical papers examining media competition and
information transmission that are related to our study, and bear directly on our
results. Many of these papers are ‘demand driven,’ that is in the model consumer
have a ‘taste for bias’ or behavior characteristic that induces firms in equilibrium
to adopt different viewpoints as part of a profit maximizing strategy. The firms
themselves have no agenda per se but adopt a viewpoint to capture a segment of
the media market. Mullainathan and Shleifer (2005) is perhaps the canonical ”de-
mand side” media bias model. It builds on the behavioral economics work of Rabin
and Schrag (1999) on what is called “self-confirmatory bias.” That is, a decision
maker may have a “first impression” bias towards one position or another and in
collecting information in the decision-making may receive utility from receiving in-
formation that confirms the prior belief or bias. This type of model of consumer
9
behavior is adopted in their study, and they examined the impact of competition
when consumers are distributed with certain biases (some people prefer left-wing
information while others prefer right-wing information). They find that the market
will be characterized by polarization, with firms offering different viewpoints that,
in equilibrium, will be biased. Although this model is interesting, it has two lim-
itations from the point of view of the FCC’s exercise in examining the role of the
media ownership rules. The first problem is that it is very difficult to do any type
of economic welfare analysis in these models. Self-confirmatory bias comes from
preferences and so it is unclear whether the FCC should consider these biases at
all and if it should, whether it is a good thing or a bad thing from the diversity of
the viewpoint perspective. Are the perspectives being offered something akin to the
diversity of flavors of ice cream or should we think that the diversity of viewpoint be-
ing offered here increases polarization in society and leads people to make ineffectual
decisions? Baron (2006) demonstrates that this can be the case. The second issue
with the Mullainathan and Shleifer model is that, as we shall discuss further, there
is a second type of cognitive bias embedded in the model. Indeed, when consumers
do not receive the correct signal agents do not make the inference that should be
made given the media bias. The model developed below with fully rational agents
incorporates exactly these features. Therefore, although Mullainathan and Shleifer
(2005) is illustrative, we think that it has little to say on the FCC proceedings. In
particular the lack of the ability to make welfare analyses means that although the
authors of this study can say how market structure affects the equilibrium, they
are unable to make any definitive judgments as to whether or not this is in the
public interest. Finally, we are also unconvinced that behavioral biases are the sole
(or even the major) factors driving viewpoint diversity. The papers by Gentzkow
and Shapiro (2006), Baron (2006), and Bernhardt, Krasa, and Polborn (2008) also
analyze media market with demand driven media slant or viewpoint. Baron (2006)
is able to provide welfare analysis in his model and finds a role for regulation. In
Gentzkow and Shapiro (2006), bias is driven by media outlets trying to gain their
reputation by reinforcing a viewer’s prior belief rather than a behavioral bias per-se.
Like in our study, consumers in that model are rational in that they correctly update
their belief upon seeing an uninformative signal.
The closest paper to the current study is the paper by Anderson and McLaren
(2010). In particular, they build a “supply side bias” model where the media owners
may choose to transmit information or bias the signal by withholding information
to the decision maker in equilibrium. The decision maker/consumer is also rational
in the sense that she makes the correct inference upon seeing an uninformative
signal. The paper characterizes the equilibrium with a single owner of the media
10
outlets and compare that with the introduction of a second owner. They find that
competition increases the amount of information transmitted and the diversity of
viewpoint. Their model is closely related to our Model 1 below. However, they
also include price competition, so our Model 1 can be seen as a special case of their
model. Unsurprisingly, our results and conclusions are very similar. Gentzkow and
Shapiro (2006) also develop a model where consumers do update correctly and so
our models are similar to theirs. Finally, although there is costly communication in
our model, there is a link between our work and the models of “cheap talk” with
multiple senders, for example Krishna and Morgan (2001).
4 Measuring Welfare in Media Markets
4.1 Blackwell’s Theorem
The approach adopted in this study is that the media market functions as an ‘in-
formation market:’ it provides signals to a citizen, or information consumer, who
uses the signal to form a belief and choose a plan of action. We then ask when is
one market ownership structure better than another? The answer is provided by
the simple observation that if a change in ownership structure leads to better infor-
mation, this increases the utility of the consumer and therefore it is in the public
interest.
Our analysis begins with the beautiful theorem of David Blackwell (1951). An
elegant proof of Blackwell’s theorem is provided in Cremer (1982). In a classic
paper on “the comparison of experiments,” Blackwell investigated the concept of
what it means to have “better information.” Blackwell postulated two different
measures of the quality information and in a remarkable result he was able to prove
that the two different measures turn out to be mathematically equivalent. The first
measure is purely statistical, based on information theory and signal transmission
whereas the second measure is based on the intuitive economic notion that better
information is more valuable to the decision maker when it helps her make better
decisions. Blackwell’s Theorem is that one information structure is better than
another information structure under the first (statistical) criterion if and only if
it is better under the second (economic) criterion. This implies that if we can
show one media market ownership structure results in a more informative market
in the statistical sense, then it leads to higher consumer welfare, even if we do
not know the consumer’s utility function! The approach in our study is to adapt
Blackwell’s comparison of experiments to the context of media markets, that is, we
think of the media market as Blackwell thinks of an experiment. Given the firms
11
and the structure of ownership in the market, firms collect information about the
true state of the world. They then process this information and report a signal
through the television or radio station to the viewer/listener citizens. A citizen
then decides whether to receive this information, that is view the channel or listen
to the radio broadcast. Once receiving the signal, she chooses to form a path of
action (for example, who to vote for) or chooses to form a set of beliefs about
the relevant policy question, (for example, “do the social benefits of a carbon tax
outweigh the cost?”). In our paper we will not distinguish between forming beliefs
and actually taking an action. The citizens use this information to take the action
that maximizes their expected utility. That is, they wish to choose the action that
is best for them given their updated beliefs about what the true state of the world
conditioned on the information they receive through the media market. In this paper
we then ask the following questions: How does the structure of ownership affect the
transmission of information and the quality of the signal received by the decision
maker? Does the information that is received depend on the market structure or
the ownership structure and if so can we characterize the comparative statics of that
ownership structure on the quality of the decision being made by the citizen? We
continue in this section with an exposition of Blackwell’s approach and an example of
exactly how we can apply it to different market structures and levels of information
transmitted.
The Blackwell framework approaches the world as a statistical problem and
assumes that the decision maker is a rational Bayesian expected utility maximizer
as axiomatized in the classic work of Savage (1954). That is, the primary concept
here is that there is a set of states of the world, S, and a set of actions, A, that
can be chosen by a decision maker. Given that the state of the world is s and the
decision-maker chooses action a, the decision maker receives a utility of that choice
which is denoted U(a,s). The decision maker has a prior probability distribution
over the state’s p(s) where for all s ? S, p(s) ? 0 and
summationtext
s?S
p(s) = 1. Given any
choice that induces a random utility outcome over the states, the consumer chooses
an action to maximize the following expected utility function:
summationdisplay
s?S
p(s)U(s,a).
In this section will assume that the state and signal spaces are finite. However, this
is only to aid the exposition. In the following sections we will use convex compact
state spaces and continuous probability measures rather than sums, but the concepts
are the same.
There is a set of possible signal outcomes denoted T with generic element t. An
experiment or signal or in our context media information transmission, is a random
12
variable or a n × k Markov Matrix [X] where x
ts
is the probability of observing
signal t when the true state of the world is s. That is, for all (t,s) x
ts
? 0 and for
all states s ? S
summationtext
t?T
x
ts
= 1.
Given a signal matrix [X], a decision maker will upon observing the signal out-
come t update her belief about the probabilities of the true state q(s|t), that is, form
a posterior distribution via Bayes Law. She will then choose an action to maximize
her expected utility:
max
a?A
summationdisplay
s?S
q(s|t)U(a,s).
Let the path of action a
?
(X,t) be the solution to the maximization problem,
that is the optimal action given information structure [X] after observing signal t.
Define the value of experiment or information structure [X] as:
V(X)=
summationdisplay
t?T
summationdisplay
s?S
x
ts
U(a
?
(X,t),s).
under the economic criterion, we will say that X
1
is more informative than X
2
or X
1
followsequal X
2
if V(X
1
) ? V(X
2
), that is if the decision maker has at least as high an
expected utility upon acting on the signal X
1
as acting on the signal X
2
. Blackwell’s
statistical definition follows. We will say that X
1
is a sufficient statistic for X
2
, or
X
1
? X
2
, if [X
1
][M]=[X
2
] for some Markov matrix M. Intuitively this means
that X
2
is equal to X
1
plus some noise.
We can now state the theorem:
Proposition 1 Experiment [X
1
] is more informative than experiment [X
2
] if and
only if [X
1
] is a sufficient statistic for [X
2
]. That is, X
1
followsequal X
2
if and only if
X
1
? X
2
To illustrate the power of this approach, consider a simple example where the
decision maker must choose between two actions “High” and “Low.” There are two
states of the world. In state s
H
, High is the optimal action and in state s
L
, Low is
the optimal action. Assume that the utility of choosing the optimal action is 1 and
the utility of choosing the suboptimal action is 0. Suppose that signals can have
three values High, Medium or Low. The prior belief is that each state is equally
likely. Consider the two experiments [X] and [Y] below.
TABLE A.4a: Signal [X]
x
H
x
M
x
L
s
H
1/2 1/2 0
s
L
0 1/2 1/2
13
TABLE A.4b: Signal [Y]
y
H
y
M
y
L
s
H
1/3 1/3 1/3
s
L
1/3 1/3 1/3
In this case [X] is preferred to [Y]. To see this, consider observing the signal
x
H
. The agent knows that the true state is s
H
and so the agent chooses “High.”
Similarly if the agent observes s
L
she knows the state is s
L
and she choose Low.
Observing X
2
she knows each outcome is equally likely, so she randomizes. Notice
that the subject picks the optimal action 75% of the time. Now consider experiment
[Y]. As it is equally likely that that signal was generated in either state, the signal
provides the subject no basis to revise her prior and so the optimal action is to just
pick an action independent of the signal (or randomize). Thus under experiment
[Y] the agent makes the correct decision with probability 50%. Therefore, she has
a lower level of expected utility.
The most informative signal of course is where we learn every state precisely,
called “Full Information. “ We will refer to a full information signal as [I] because
such a signal is equivalent to the Identity matrix where there is a re-labeling of states
after we eliminate redundant signals. The matrix of probabilities is the matrix I with
1 on all the diagonal elements and 0 for all the off-diagonal entries. In this case, the
signal spans the state space. The opposite extreme is the example [Y] above, that
is the matrix where every element is 1/n. In this case, we learn nothing from the
signal and the decision maker continues to hold her prior belief after every signal.
That signal will be labeled [J] for jamming signal although we could also label it a
Spamming Matrix as it spans the null space. It will be shown in the next section that
the media outlets will either use [I] or degenerate uninformative signal as conditional
signals.
TABLE A.4c: Signal [I] “Full Information”
I
H
I
M
I
L
s
H
1 0 0
s
L
0 0 1
TABLE A.4d: Spamming Matrix [J]
1/3 1/3 1/3
1/3 1/3 1/3
1/3 1/3 1/3
14
Now notice that [X] · [J]=[Y], that is we obtain experiment [Y] by applying
the operator [J] to [X] which dilutes the information transmission.
It is worth reminding the reader at this point what we do not need to know to
make welfare comparisons. In particular Blackwell’s Theorem does not require us
to know the utility function, the decision maker’s prior preference, or her beliefs.
If we can show that one experiment is a sufficient statistic for another, then it is
welfare improving. In the following we demonstrate that we can use this insight to
rank equilibria in media markets. Therefore in the models and experiments below
we can in a precise manner state arguments like “a market with four independent
firms is better than with two” and “in our experiments, the market with six firms
performed better than the market with four firms. “
4.2 Strategic Information Disclosure
Blackwell’s Theorem provides us with a methodology to evaluate the quality of
information transmitted in a market, but it assumes that the signal comes from a
neutral source rather than a firm that may have an agenda. The link to an economic
model is provided by the seminal works of Milgrom (1981), Grossman (1981) and
Jovanovic (1982). In Milgrom’s model one agent (a sender, who we can think of as a
salesman) has observed the value of a random variable x ? X and chooses to make
a report to a second agent (a receiver, who we can think of as a buyer). Given the
information, the buyer then must make a decision to purchase a good or not. The
higher the value of x the higher the quality of the good and the more valuable it is
to the buyer. The salesman can report any signal that contains the truth, but only
earns a commission if the buyer buys. Thus the salesman would like to bias the buyer
towards a purchase. We assume that he can report any R ? X with x ? R. Thus,
the salesman cannot deliberately lie but can be very uninformative by reporting a
large R. Notice in particular that if R ? R
prime
then report R is more informative than
report R
prime
in Blackwell’s sense. Milgrom’s remarkable result is that the salesman
should report the simple truth, x. The logic is known as “unraveling.” That is, if
they buyer sees some set R he knows the true value is in R and so she will form some
expectation of the true value in that set. But such an expectation will be below the
largest element in R and so the true value cannot be the maximum -otherwise the
salesman should have just reported that maximum point and thereby increased the
chance of a sale - but then it cannot be the second highest point in R either, and
so on... In equilibrium, the only consistent beliefs are that on seeing a set R the
truth is the worst point in R. That is, “no news is bad news.” This leads to the
paradoxical conclusion that the salesman cannot gain by withholding information.
15
In our context, it means that even with a monopoly information provider who has
an incentive to manipulate the decision maker, the equilibrium is full information
revelation and therefore by Blackwell’s Theorem, fully efficient! The key innovation
that Milgrom developed is to have the decision maker correctly condition on what
she does not know given the incentives of the sending party. The implication of
this analysis for media market is drawn out in a subsequent paper by Milgrom and
Roberts (1986) who note that “it has been argued that free and open discussion
or competition in the market for ideas will result in the truth being known and
appropriate decisions being made and this feature arises naturally in our model.”
However, Milgrom’s unraveling result depends on some strong key assumptions.
In particular the buyer/decision maker knows the bias of the sender, the information
structure is common knowledge, and the sender always knows the true value of x.
If there is some small probability that the sender does not know the true value then
we shall show that complete unraveling fails. Finally there is the “grain of truth”
assumption that the sender cannot deliberately mislead the receiver by giving false
information- only fuzzy information is allowed. In the following models we will adapt
Milgrom’s model to the case of media competition, but relax his key assumptions.
First we will allow for the possibility that there is “no news” so that when an
uninformative signal is observed it could simply be that the sender is uniformed.
In our second model we will allow for some specific type of “disinformation” or
signal jamming, such that one media firm can confuse the voter -at a cost- by
contradicting the signal sent by another media outlet. With these adaptations we
find that unraveling still occurs but not to a full extent and that, in equilibrium, the
media will either be fully informative or uninformative. Therefore, by Blackwell’s
theorem all we have to do is measure the size of the set of states of the world where
the signal is uninformative. If competition shrinks this set then it automatically
increases welfare.
In addition to the seminal literature and works on media bias per se, there is re-
lated recent literature on product information disclosure in Industrial Organization
and Marketing. Prominent recent papers include Sun (2010), Guo and Zhao (2009),
and Board (2009). Sun deals with both horizontal product information (using the
classic linear city model, witha monopolist of unknown location) and a quality di-
mension: first quality is assumed known, and then it isassumed unknown, although
in the latter case she assumes that the firm must disclose either all information or
none at all –she does not allow the decisions to be split up. Guo and Zhao (2009)
address duopolists’ incentives to reveal quality information, under the assumption
that each is ignorant of the other’s quality; Board (2009) does similarly assuming
that theyknow each other’s quality. The model we develop below is closely related
16
Board (2009).
5 Model Preliminaries
In the next sections we build three models to analyze the incentives of media outlets
to withhold, garble or otherwise bias the information transmitted. All the models
have a common basic structure which is developed here.
Consider two media outlets, or editors, that support opposite political policies
or parties, A and B (media outlets and candidates will be indexed by i and j with
i negationslash= j). With opposite editorial or political views, the media may be competing to
influence citizens or decision makers who may be thought of as information con-
sumers or voters. From now on, we will use the canonical case of parties and voters,
although one should keep in mind that media outlets are the vehicle to express the
information of parties. In particular, we adopt the model used in Political Science
known as electoral competition with “ideology” and “valence.” That is, there is a
one dimensional policy space ranging from “Left” to “Right” and each voter has an
ideal point or most preferred policy in that interval. For example we might think of
the level of social service expenditure and taxation. Some voters will prefer a higher
level of expenditure (and therefore high taxes) while other voters will prefer a lower
level of expenditure (and lower taxes). The are two options, one of which must be
chosen. We can think of political parties committed to implement these different
policies. However, following Stokes (1963) the decision maker also cares about the
quality or competence of the elected official. This property is known as “valence”
in the political economy literature (see e.g., Groseclose (2001)). Thus voters have
preferences over both the policy position of the parties and the quality or valence of
each of the candidates. In particular a rational voter would prefer a competent- or
high valence- official even if the policy is far from her ideal point, over an incompe-
tent -or low valence- official who would implement a policy closer to her ideal. It is
well known that in these spatial models with a majority rule electoral competition,
the beliefs and preferences of the median voter determines the electoral outcome.
Therefore it is common, even though we have in mind a large number of voters, to
focus on the decision of a single citizen, the median voter, as it is the competition
for the median voter that determines the final outcome. Formally, we introduce the
following elements.
• Quality or valence. The valence or quality of candidate i is ?
i
? [?,?]. We
assume that ?
i
is drawn from a distribution with c.d.f. F
i
(?
i
).
• Location or ideology.The policy space is the unit interval [0,1]. It is common
17
knowledge that Media outlet A supports the candidate located at z = 0 and Media
outlet B supports the candidate located at z = 1.
• Voters’ preferences. For simplicity, we assume there is only one voter who is
located at z ? [0,1]. The utility for the voter of supporting candidate i is equal
to the candidate i’s quality minus the Euclidian distance between the voter’s ideal
position and the position of the candidate i. Formally, u
z
(A)=?
A
?z if candidate A
is elected and u
z
(B)=?
B
?(1?z) if candidate B is elected. Given such preferences
a voter strictly prefers to elect candidate A if he is located at z < z
?
and candidate
B if he is located at z > z
?
where z
?
is given by:
?
A
?z
?
= ?
B
?(1?z
?
) ? z
?
=
1
2
+
1
2
(?
A
??
B
)
We assume that the location of the voter is random. More precisely, z is drawn
from a uniform distribution z ? U[0,1]. Naturally and as mentioned earlier, it is
formally identical to consider a continuum of voters with z representing the location
of the median voter.
• Media owners’ preferences. Candidates only care about winning the election.
Each media owner is interested in the probability that her preferred candidate (or
viewpoint) wins. Denote by
˜
?
i
candidate i’s expected quality inferred by the voter.
As we will develop below, this quality may or may not coincide with the exact
quality of candidate i. This inferred quality is what the voter uses for his decision.
The utility of media outlet i, ?
i
, is simply the probability that candidate i wins the
election given the inferred qualities of both candidates:
?
A
= Pr[z < z
?
]=
1
2
+
1
2
(
˜
?
A
?
˜
?
B
) and ?
B
= Pr[z > z
?
]=
1
2
+
1
2
(
˜
?
B
?
˜
?
A
)
6 Model I: Disclosure under the veil of ignorance
6.1 Information and disclosure
Consider a situation where there are two media outlets, each of which has a “view-
point.” Formally, media outlet i would prefer to see a particular candidate i win
the election. However the media outlet may not know the candidate’s quality. More
precisely, consider the following setting.
• Information. Media outlet i observes the exact quality of the candidate it sup-
ports with probability 1?p
i
(signal ?
i
= ?
i
) and it observes nothing with probability
p
i
(signal ?
i
= ?
i
).
18
• Disclosure. We take a very simple approach to disclosure. We assume that
media outlets can withhold information regarding candidate i but cannot report
false or inaccurate information. More precisely, the report r
i
(?
i
) of media outlet i
given his signal is r
i
(?
i
)=?
i
and r
i
(?
i
) ? {?
i
,?
i
}. This means that whenever ?
i
is
observed, the media outlet has to choose between full or no disclosure. In particular
and only for simplicity, partial disclosure (e.g., reporting an interval R
i
such that
?
i
? R
i
) is not an option.
• Timing. We consider the following timing. First, nature chooses ?
A
and ?
B
and communicates ?
i
? {?
i
,?
i
} to media outlet i. Second, parties simultaneously
choose r
i
(?
i
). Third, the voter observes (r
A
,r
B
), updates his beliefs
˜
?
A
and
˜
?
B
and
chooses which candidate i to vote for.
6.2 Equilibrium
First, notice that by definition r
i
(?
i
)=?
i
. Therefore, we only need to determine
r
i
(?
i
). Second, media outlet i’s utility is increasing in
˜
?
i
and decreasing in
˜
?
j
, that
is, a media outlet benefits when the perceived quality of his preferred candidate
is high and the perceived quality of the rival candidate is low. In fact, given ?
i
,
the objective function of media outlet i is to maximize
˜
?
i
. Third, suppose that the
equilibrium involves r
i
(?
i
)=?
i
if ?
i
? ?
i
and r
i
(?
i
)=?
i
if ?
i
negationslash? ?
i
, where we put
a priori no restrictions on the set ?
i
. It is immediate that the expected utility of
media outlet i given signal ?
i
= ?
i
, ?
i
(?
i
), satisfies the following properties:
?
i
(?
i
)=?
i
(?
prime
i
) ??
i
,?
prime
i
negationslash??
i
and ?
i
(?
i
) ??
i
(?
prime
i
) ??
i
,?
prime
i
??
i
with ?
i
> ?
prime
i
Indeed, when media outlet i reports ?
i
, the voter’s belief
˜
?
i
cannot depend on the
realized quality. Conversely, when media outlet i reports ?
i
, the belief becomes the
true quality ?
i
. These properties imply that if ?
i
negationslash? ?
i
then ?
prime
i
negationslash? ?
i
for all ?
prime
i
< ?
i
and if ?
i
? ?
i
then ?
primeprime
i
? ?
i
for all ?
primeprime
i
> ?
i
. In other words, the optimal strategy of
media outlet i must necessarily be a cutoff strategy, where there exists x
i
? [0,1]
such that:
r
i
(?
i
)=
braceleftbigg
?
i
if ?
i
? [0,x
i
)
?
i
if ?
i
? [x
i
,1]
We can now determine the optimal cutoffs(x
A
,x
B
). The first step consist in
determining the posterior belief distribution of consumers when information is not
reported. We have:
f
i
(?
i
|r
i
= ?
i
)=
Pr(r
i
= ?
i
|?
i
)f
i
(?
i
)
integraltext
1
0
Pr(r
i
= ?
i
|?
i
)f
i
(?
i
)d?
i
19
and therefore:
f
i
(?
i
|r
i
= ?
i
)=
f
i
(?
i
)
integraltext
x
i
0
f
i
(?
i
)d?
i
+ p
i
integraltext
1
x
i
f
i
(?
i
)d?
i
if ?
i
<x
i
f
i
(?
i
|r
i
= ?
i
)=
p
i
f
i
(?
i
)
integraltext
x
i
0
f
i
(?
i
)d?
i
+ p
i
integraltext
1
x
i
f
i
(?
i
)d?
i
if ?
i
>x
i
The expected value of ?
i
inferred by consumers when information is not reported
and given a cutoff x
i
is then:
E
i
[?
i
|?
i
;x
i
]=
integraltext
x
i
0
?
i
f
i
(?
i
)d?
i
+ p
i
integraltext
1
x
i
?
i
f
i
(?
i
)d?
i
integraltext
x
i
0
f
i
(?
i
)d?
i
+ p
i
integraltext
1
x
i
f
i
(?
i
)d?
i
=
p
i
E
i
[?
i
] + (1?p
i
)
integraltext
x
i
0
?
i
f
i
(?
i
)d?
i
p
i
+ (1?p
i
)F
i
(x
i
)
= µ
i
E
i
[?
i
] + (1?µ
i
)E
i
[?
i
|?
i
<x
i
] where µ
i
=
p
i
p
i
+ (1?p
i
)F
i
(x
i
)
That is, the expected posterior is a weighted average of the expected prior and
the expected posterior conditional on the media outlet having the information and
deciding not to disclose it. The weights are given by the likelihood of not receiving
the information and the likelihood of receiving the information but deciding not to
disclose it.
The equilibrium of the disclosure game is the value x
i
such that:
2
x
i
= E
i
[?
i
|?
i
;x
i
] (1)
Indeed, if the voter anticipates a cutoffx
i
, the utility of media outlet i is
1
2
(1+?
i
?
˜
?
j
)
if r
i
(?
i
)=?
i
and
1
2
(1 + E
i
[?
i
|?
i
;x
i
] ?
˜
?
j
) if r
i
(?
i
)=?
i
. Since, by construction,
E
i
[?
i
|?
i
;x
i
] is independent of ?
i
, Media outlet i strictly prefers to report r
i
(?
i
)=?
i
for all ?
i
<x
i
and r
i
(?
i
)=?
i
for all ?
i
>x
i
. The properties of the equilibrium cutoff
as a function of the probability that the media outlet does not get the information,
x
i
(p
i
), are summarized below.
Proposition 2 The cutoff x
i
(p
i
) is unique, increasing in p
i
and such that x
i
(0) = 0
and x
i
(1) = E
i
[?
i
].
2
This result is reminiscent of Dye (1985), although in that paper the conditional expectation is
derived heuristically and it turns out that the condition is incorrectly specified. It is also implied
by the results of Anderson and McLaren (2010).
20
Proof. Let A(x
i
)=p
i
x
i
+(1?p
i
)x
i
F(x
i
)?p
i
E
i
[?
i
]?(1?p
i
)
integraldisplay
x
i
0
?
i
f(?
i
)d?
i
. Equation
(1) can be rewritten as A(x
i
) = 0. Notice that A(0) = ?p
i
E
i
[?
i
] ? 0, A(1) =
1 ? E
i
[?
i
] > 0 and A
prime
(x
i
)=p
i
+ (1 ? p
i
)F(x
i
) > 0, which together proves the
uniqueness. Also, let
B(P
i
)=
P
i
E
i
[?
i
]+
integraltext
x
i
0
?
i
f(?
i
)d?
i
P
i
+ F
i
(x
i
)
with P
i
=
p
i
1?p
i
Equation (1) can be rewritten as x
i
= B(P
i
). Hence,
dx
i
dp
i
? B
prime
(P
i
)=
F
i
(x
i
)
[P
i
+ F
i
(x
i
)]
2
parenleftBig
E
i
[?
i
]?E
i
[?
i
|?
i
<x
i
]
parenrightBig
> 0
Finally, x
i
(0) = 0 and x
i
(1) = E
i
[?
i
] are obtained immediately from (1). a50
The intuition behind Equation (1) and Proposition 2 are simple. If parties
always know their quality (p
i
= 0), the standard no-news-is-bad-news unraveling
argument of Milgrom (1981) and Milgrom and Roberts (1986) holds: the media
outlet always has an interest in revealing the quality of a highest type candidate i,
then so does the media outlet with a candidate of second highest quality, and so
on. In equilibrium this implies full revelation (this result has been experimentally
documented in Forsythe, Isaac and Palfrey (1989)). When p
i
> 0, media outlets who
know that their favorite candidate has low quality may pool with uninformed media
outlets and choose not to disclose their information. In that case, no information
revelation may occur in equilibrium even in the absence of a disclosure cost.
3
As
media outlets become more likely to be (exogenously) uninformed, the incentives of
informed media outlets to pool are higher, so the cutoff x
i
increases. When media
outlets almost never obtain information (p
i
? 1) voters infer the expected quality,
so any media outlet i would choose not to disclose the quality of any candidate
below E
i
[?
i
]. Finally, notice that the utility of media outlets, ?
i
, is additively
separable in the inferred qualities of both candidates, (
˜
?
i
,
˜
?
j
). Therefore, there are
no strategic considerations in the disclosure game, that is, the incentives to withhold
information of one media outlet i do not depend on the disclosure decision of the
other. In the next section, we will test whether informed subjects effectively choose
to pool with uninformed ones in a controlled laboratory setting. These results are
similar to those in Anderson and McLaren (2010). In that paper they also use a
similar welfare measure to ours, although they include pricing for the media, they
3
However, as shown by Anderson and McLaren (2010), this strategy can backfire when there
truly is no news, and the media suffers from the “suspicion effect”.
21
show that welfare increases with two media outlet owners versus a single monopolist
owner who will supply only one viewpoint. A similar result obtains in our model.
We finally illustrate the result with a simple analytical example.
Example 1 Suppose that ?
i
? U[0,1]. Equation (1) becomes:
x
i
=
p + (1?p)x
2
i
2p + 2(1?p)x
i
? x
i
=
?
p?p
1?p
7 Model II: Disclosure under the threat of sabo-
tage
7.1 Information and disclosure
Consider the same setting as in section 5 and assume for simplicity that media
outlets always observe the quality of candidates (p
i
= 0).
• Disclosure. Just like before, media outlet i can decide whether to disclose
(r
i
i
(?
i
)=?
i
) or withhold (r
i
i
(?
i
)=?
i
) the information regarding the quality ?
i
of
candidate i. The new option is that, in case of disclosure, media outlet j can now
choose whether to allow (r
j
i
(?
i
)=?
i
) or garble (r
j
i
(?
i
)=?
i
) the information regard-
ing candidate i. If media outlet i discloses and media outlet j allows information,
then the voter learns ?
i
. Conversely, if media outlet i withholds or media outlet i
discloses but media outlet j garbles the information, then the voter obtains no in-
formation. Information garbling captures the idea that a media outlet i can confuse
the voters by adding noise to the news revealed by the opposing media outlet j.
The situation is symmetric for media outlet j. To the best of our knowledge, this
option is quite prevalent and yet has never been modeled in the literature before.
4
It is crucial to notice that, in the absence of information, the voter cannot determine
whether it is due to withholding by a media outlet i or garbling by the opponent.
Also, media outlet j cannot reveal information that has been withheld by media
outlet i.
• Costs. We assume that media outlet i has a cost d
i
/2 of withholding his infor-
mation whereas media outlet j has a cost c
i
/2 of garbling the information of media
outlet i. In our view, it seems natural to assume that a media outlet needs to spend
4
For example there are many websites with respectively left wing or right wing viewpoints that
claim to document instances of misrepresentation by the media outlets.
22
resources to try and “mislead” the voter by either withholding evidence about him-
self or suppressing evidence about the opponent. However, our model encompasses
other cases. Indeed, a cost to disclose a media outlet i’s own information would
simply correspond to a negative d
i
and a cost to allow the other media outlet’s
information would correspond to a negative c
i
. In particular we can think of these
costs as reputation costs. That is, if the consumer learns that the firm has garbled
or biased information, then it is an unreliable source and so the consumer is less
likely to view or listen to that channel or station in the future, and so the firm’s
audience share and profits will fall.
• Timing. The new timing of the game is the following. First, each media
outlet decides whether to disclose or withhold information about its own candidate.
Second, if information is disclosed, the other media outlet decides decide whether to
allow or garble that information. Third, the voter observes the information if and
only if it was both disclosed and allowed. Otherwise she observes nothing and in
particular cannot infer whether information was withheld or garbled. In either case,
she decides which candidate to support.
7.2 Equilibrium
Consider the case c
i
? 0 and d
i
? 0. As in Model I, qualities are additively separable
in the voter’s utility function, so the incentives by either media outlet to act on the
information of one candidate is independent of the quality of the other candidate.
However and as we will see below, the incentives to withhold one’s information will
depend on the garbling strategy of the rival.
Following an analogous reasoning as in section 6, it is straightforward to notice
that both media outlets i and j have cutoff strategies regarding the decision to
withhold and suppress information on candidate i’s quality. Formally:
r
i
i
(?
i
)=
braceleftbigg
?
i
if ?
i
? [0,y
i
)
?
i
if ?
i
? [y
i
,1]
and r
j
i
(?
i
)=
braceleftbigg
?
i
if ?
i
? [0,y
i
)
?
i
if ?
i
? [y
i
,1]
This means that, in equilibrium, the voter learns ?
i
if and only if ?
i
? [y
i
,y
i
]. In
turn, it implies that the expected quality of media outlet i conditional on the voter
not obtaining information is:
E
i
[?
i
|?
i
,?
i
;y
i
,y
i
]=E
i
bracketleftBig
?
i
|?
i
? [0,y
i
]?[y
i
,1]
bracketrightBig
=
integraltext
y
i
0
?
i
f
i
(?
i
)d?
i
+
integraltext
1
y
i
?
i
f
i
(?
i
)d?
i
F
i
(y
i
) + (1?F
i
(y
i
))
= ?
i
E
i
[?
i
|?
i
<y
i
] + (1??
i
)E
i
[?
i
|?
i
> y
i
] where ?
i
=
F
i
(y
i
)
F
i
(y
i
)+(1?F
i
(y
i
))
23
The equilibrium of the withholding/garbling information game is given by the
pair of cutoffs(y
i
,y
i
) that solves the following system of equations:
E
i
[?
i
|?
i
,?
i
;y
i
,y
i
]?y
i
= d
i
(2)
y
i
?E
i
[?
i
|?
i
,?
i
;y
i
,y
i
]=c
i
(3)
In words, media outlet i prefers to withhold information if the resulting belief
about his quality net of the withholding cost, E
i
[·] ? d
i
, is greater than his true
quality ?
i
. The cutoff y
i
in equation (2) corresponds to the indifference point. Using
a similar argument, Media outlet j garbles information when the negative impact in
his utility of the belief and the cost, E
i
[·]+c
i
, is smaller than the negative impact
of allowing the true quality ?
i
to become known. Again, the cutoff y
i
in equation
(3) corresponds to the indifference point. Notice that the choices of media outlets i
and j are interrelated: media outlet i’s cutoff affects the belief under no information
which itself has an effect on j’s cutoff, and viceversa. The properties of the cutoffs
as a function of the costs of garbling and withholding, y
i
(c
i
,d
i
) and y
i
(c
i
,d
i
), have
some interesting properties that are summarized below.
Proposition 3 The cutoffs y
i
and y
i
are unique. When both the cost of gar-
bling and the cost of withholding are nil, no information ever reaches the voter:
y
i
(0,0) = y
i
(0,0) = E
i
[?
i
]. As either cost increases, there is both less garbling and
less withholding: dy
i
/dc
i
< 0, dy
i
/dc
i
> 0, dy
i
/dd
i
< 0, dy
i
/dd
i
> 0.
Proof. Let (?) denote the situation where no information reaches the decision maker.
If B reveals ?
B
, A finds it optimal to garble when:
1
2
+
1
2
(?
A
?E
B
(?))?
c
2
>
1
2
+
1
2
(?
A
??
B
) ? ?
B
> y ? E
B
(?)+c
Provided A does not garble, it is optimal for B to reveal if
1
2
+
1
2
(?
B
??
A
) >
1
2
+
1
2
(E
B
(?)??
A
)?
d
2
? ?
B
<y? E
B
(?)?d.
Note that E
B
(?)=E
bracketleftbig
?
B
|?
B
? [?
B
,y]?[y,?
B
]
bracketrightbig
and we have the following equality:
y + d = E
bracketleftbig
?
B
|?
B
? [?
B
,y]?[y + d + c,?
B
]
bracketrightbig
or, equivalently:
H(y,d,c)=(y + d)[F(y)+1?F(y + d + c)]?
integraldisplay
y
?
B
sf(s)ds?
integraldisplay
?
B
y+d+c
sf(s)ds =0.
24
We consider two cases.
Case 1: c>0 and d>0. We have H(?
B
,d,c) > 0 and therefore y < ?
B
. Moreover
H(?
B
,d,c)=d(1?F(d+c))?
integraltext
?
B
d+c
sf(s)ds is increasing in d. Let
ˆ
d the point such
that H(?
B
,
ˆ
d,c) = 0. For all d<
ˆ
d we have y > ?
B
, and for all d>
ˆ
d, we have
y = ?
B
. Note also that
?H
?y
= F(y) + 1?F(y + d + c)+df (y)+cf(y + d + c) > 0,
?H
?d
= F(y)+1?F(y+d+c)+cf(y+d+c) > 0 and
?H
?c
= cf(y+d+c) > 0. Whenever
the solution is interior (i.e. when d<
ˆ
d), we have H(y,d,c) = 0. Differentiating this
equation with respect tod(respectivelyc), it comes immediately that the equilibrium
lower cutoff y(d,c) is increasing in both c and d. Last, the equilibrium higher cutoff
is y(d,c)=y(d,c)+d + c and it is increasing in both d and c.
Case 2: c>0 and d<0. Note first that the problem is well defined if d+c>0 (to
guarantee that y < y). In that case H(?
B
,d,c) < 0 and therefore y > ?
B
. We have
H(?
B
,d,c) = 1+d?
integraltext
?
B
?
B
sf(s)ds which is increasing in d. Let
˜
d the point such that
H(?
B
,
˜
d,c) = 0. For all d<
˜
d we have y = ?
B
, and for all d>
˜
d, we have y < ?
B
.
We still have
?H
?d
> 0 and
?H
?c
> 0 but
?H
?y
? 0. As long as d is small enough, the
equilibrium lower cutoff y(d,c) is still increasing in both c and d. The equilibrium
higher cutoff is now decreasing in d and its variations with c are ambiguous. a50
As stated in Proposition 3, the solution to the system of equations (2) and (3)
has a unique solution for any distribution F
i
(·). Also, when both parties can with-
hold and garble quality at no cost, then no information gets ever transmitted to
the voter, again independently of the distribution from which the quality is drawn.
Indeed, media outlet i has always incentives to withhold the worst possible infor-
mation of candidate i and media outlet j to garble the best possible information of
candidate i (and viceversa for information regarding candidate j). An unraveling
argument applies simultaneously to both sides, which results in a complete sup-
pression of information by one of the media outlets. Not surprisingly, as the cost
of information withdrawal increases, media outlet i has less incentives to withhold
average information, which formally results in a decrease in the cutoff y
i
. More
interestingly, this decrease in y
i
implies less incentives for media outlet j to garble
information. Indeed, when no information reaches the voter, it may mean either
very low quality (withheld by media outlet i) or very high quality (garbled by media
outlet j). If media outlet i withholds less information then no information is more
likely to reflect high quality. In other words, the expected quality of media outlet i
conditional on no information reaching the voter increases. This in turn means that
garbling information is relatively less profitable for media outlet j, who therefore
25
has less incentives to do so. Formally, y
i
increases. We illustrate the result with a
simple example.
Example 2 Suppose that ?
i
? U[0,1]. Equations (2) and (3) become:
y
2
i
+ (1?y
2
i
)
2y
i
+ 2(1?y
i
)
= y
i
+ d
i
and
y
2
i
+ (1?y
2
i
)
2y
i
+ 2(1?y
i
)
= y
i
?c
i
? y
i
=
(1?d
i
)
2
?c
2
i
2
and y
i
=
1+d
2
i
?c
2
i
+2c
i
2
8 Model III: Disclosure, Competition and Repu-
tation Costs
Now we consider that the costs introduced in the last section are indeed reputation
costs. That is, there is some loss in audience share for any media outlet that engages
in biasing or garbling of information. However, our key point is that the consumer
must be able to learn who is the “garbling” media outlet and which media outlet is
being informative.
Suppose that the market structure has just two firms, one representing each
viewpoint. If media i provides an uninformative signal regarding candidate i (i.e., it
withholds information) the consumer cannot turn to media j to get that information
(and similarly with candidate j). Suppose now that there are four firms, with two
firms of each viewpoint. Suppose also that media outlets 1 and 2 favor candidate
A and firms 3 and 4 favor candidate B. In addition suppose that the consumer
faces a (perhaps very small) cost of getting multiple sources of information from the
same viewpoint. Assume that if the consumer is indifferent between two information
sources then she randomizes and views either with a 50/50 probability. We will call
this the assumption of “Informational Bertrand Competition.” We augment the
model with a value of the audience M for each viewpoint. If a single firm captures
all the audience for that viewpoint then it earns M in addition to the payoff above.
If both firms capture an audience then the payoff is M/2. Suppose now that firms
1 and 2 choose different cutoff strategies, in particular y
1
<y
2
. That is, firm 1
is more informative than firm 2 even though they both have the same viewpoint.
In equilibrium, the consumer is aware of the strategies being played by the firms
(although not the value of the private information), and given the cost of multiple
sources will choose firm 1. Note that there is no benefit from a second sourcing with
firm 2 because whenever firm’s 1 signal is uninformative, so is firm 2’s. Therefore we
26
conclude that (i) the strategy of firm 2 cannot influence the decision maker, and (ii)
firm 2 receives no audience share. Thus, there is no benefit from biasing the decision
maker and firm 2 incurs the cost of lost market share. But now consider any interior
point where the firms are splitting the audience 50/50. If firm 1 was to change its
strategy so that it becomes informative on a slightly larger set then it would now
capture 100% of the market, and the set of signals on which the consumers action
changes can be made arbitrarily small. Thus we cannot have an equilibrium with
incomplete information transmission. We have established the following result.
Proposition 4 Suppose that there are multiple firms with the same viewpoint and
in the equilibrium some information is transmitted. Then the cutoffs y
i
and y
i
are
unique and identical for firms with the same viewpoint. Moreover under Informa-
tional Bertrand Competition the equilibrium becomes fully revealing, that is, all firms
transmit their information for every signal.
Proof. Consider firms 1 and 2 and fix the strategies of firms 3 and 4. If both
firms have an audience then the consumer must be indifferent between firm and
1 and 2. Now fix y
1
and y
2
and assume that y
1
<y
2
. Then notice that if the
consumer was indifferent between firms 1 and 2 if firm 2 lowers y
2
then the consumer
will receive more information and so receive a higher expected utility from firm
2. Therefore, the consumer will choose to get information from firm 2 exclusively
which increases firm 2’s utility by M/2. However firm 2 also saves the incremental
cost of withholding on a smaller set and at the first order conditions for y
2
at an
interior equilibrium the marginal benefit of withholding - influencing the consumers
decision- is equal to the marginal cost. Therefore, firm 2 strictly benefits from
changing its strategy. A similar argument applies to establish y
1
= y
2
. A symmetric
argument applies to firms 3 and 4. Now suppose that we have a symmetric interior
equilibrium where less than full information is being disclosed. In particular suppose
that y
1
= y
2
< 1. Then the consumer is indifferent between firms 1 and 2 and will
source her information from only one of them. Again at an interior equilibrium the
marginal cost of garbling on larger set equals the marginal gain from the incremental
probability of changing the consumers decision. However by marginally increasing
y
1
firm 1 captures all the market and so increases its profits discretely by M/2. Thus
again there will be an unraveling as firms 1 and 2 compete for market share. The
symmetric argument applies to both y
i
and firms 3 and 4. Therefore the equilibrium
involves full information revelation. a50
Informational Bertrand Competition is obviously an extreme assumption, but it
obtains a strong result: full information efficiency with two firms of each viewpoint.
27
Like the standard Bertrand model, we think of this as being a benchmark that
provides useful insights. In particular it may be that there is still an increase in
informational efficiency and social welfare as we move above 4 independent owners
or firms. That is, if consumers do not perfectly know each firm’s strategy, but rather
learn from their history of behavior it may be that there is an incremental benefit
from more competition. Similarly if firms viewpoints are drawn at random and the
existing firms in the market all have the same viewpoint then introducing a fifth
firm could add viewpoint diversity and a sixth firm with that under-represented
viewpoint will induce competition. This would result in a probabilistic increase in
welfare. To address these concerns we adopt experimental techniques, as reported
in the next sections.
9 Experimental design and procedures
We tested in the laboratory Models II and III, from now on labeled experiments 1
and 2. Although Model I provides the basic framework for our analysis we did not
test it for two reasons. First, it is closest to the existing theoretical and experimental
literature (Forsythe, Isaac and Palfrey, 1989), so the gains of a new test are smallest.
Second, it provides a reason for non-disclosure (veil of ignorance) which, in our view,
is interesting but less relevant for the application to competition and the structure of
media ownership than the other two models. Since, we are primary concerned with
the effect of media competition on information provision, we decided to concentrate
on the other two models.
We conducted 2 sessions of experiment 1 with a total of 24 subjects and 2 ses-
sions of experiment 2 with a total of 29 subjects. Sessions were conducted at the
Computer Laboratory of the Economics Department at the University of South-
ern California. Subjects were a mixed of registered undergraduate and graduate
students at the University of Southern California who were recruited with in-class
announcements and by email solicitation. All interaction between subjects was
anonymous and computerized, using an extension of the open source software pack-
age ‘Multistage Games.’
5
No subject participated in more than one session. For
each session in experiment 1, twelve subjects were randomly assigned in groups of
three for each match, with random rematching after each match. In experiment 2,
subjects were randomly assigned in either groups of five (session 3) or seven (session
4) at the beginning of the session and remained in the same group until the end of
5
Documentation and instructions for downloading the software can be found at
http://multistage.ssel.caltech.edu.
28
the experiment. Table 1 displays the pertinent details of the four sessions.
Session date experiment # subjects group size matching
1 01/19/2011 1 12 3 random
2 01/19/2011 1 12 3 random
3 01/19/2011 2 15 5 fixed
4 01/19/2011 2 14 7 fixed
Table 1: Session details
At the beginning of each session, instructions were read by the experimenter,
which fully explained the rules, information structure, and computer interface.
6
After the instructions were finished, one practice match was conducted, for which
subjects received no payment. After the practice match, there was an interactive
computerized comprehension quiz that all subjects had to answer correctly before
proceeding to the paid matches.
9.1 Experiment 1
The experimental game closely followed the Model II setting described in section
7 above. At the beginning of each match, each subject in a group was randomly
assigned a role as either A, B or C. A number was then drawn randomly from a
uniform distribution between 0 and 100. This number, called state, was disclosed to
the players with roles A and B.
7
They had to decide independently and simultane-
ously whether to disclose the state to agent C. If A (respectively B) decided not to
transmit the information, he incurred a cost c
A
(respectively c
B
) that was deducted
from his final payoff. These costs were known from all participants in the group but
they varied as will be detailed below. The state was disclosed to C only when both
A and B decided to transmit the information. If at least one agent decided not to
transmit, then C would observe “state is unknown” but not the identity of the player
responsible for the no-transmission. The act of no-transmission thus captures both
“withholding” and “garbling” in the terminology of section 7. The crucial factor is
that information remains unknown it at least one agent does not transmit it. The
6
Sample copies of the instructions are attached in the Appendix.
7
As we will see below, payoffs are constructed in a way that the state can be understood as
?
A
? ?
B
, the difference between the qualities of candidates A and B. Since ?
A
and ?
B
enter
additively in the media outlets’ utility function, considering a uni-dimensional state parameter
(? ? ?
A
??
B
) simplifies the exposition without affecting the main conclusions.
29
subject with Role C had then to choose a number between 0 and 100. The payoffs
of subjects in roles A, B and C, denominated in points, were respectively:
pi
A
= z, pi
B
= 100?z, pi
C
= 100?
(z ??)
2
40
where z is the action taken by C and ? is the state (revealed to C or not). Notice
that these payoffs constitute a reduced-form representation of the payoffs in Model
II. In particular, they imply that the participant with Role A wants to maximize
the action chosen by C, the participant with Role B wants to minimize it while
the best strategy of the participant with Role C is to choose an action equal to the
expected value of the state given the information he observes. Trivially, when the
state is disclosed, the optimal action is to choose a number equal to the true state.
We chose to endow role C with a quadratic scoring rule because we thought it was
easier to explain this reduced-form payoff rather than the more elaborate median
voter preferences. Notice that the objective was not to test whether subjects realize
that the quadratic scoring rule is “proper”, in the sense that it is optimal to report
your expected belief. Instead, we did explain in detail during the instructions that
the quadratic rule has this property and asked one question in the quiz to make sure
they understood it. The goal was to encourage subjects in role C to report their
expected belief about the state, and to encourage subjects in roles A and B to try
and bias that expected belief with their decision to transmit or not the information.
Given this design, the equilibrium strategy of all players follows the basic princi-
ples described previously. The participant with Role A should withhold low values
while the participant with Role B should withhold high values. A non-informed par-
ticipant with Role C should infer that either A or B had incentives to withhold the
state and choose the expected value taking this piece of information into account.
Subjects participated in 45 paid matches, with opponents and roles randomly
reassigned and states randomly drawn at the beginning of each match. The design
included three blocks of fifteen matches, where the cost pairs (c
A
,c
B
) were identical
within blocks and different across blocks. The three cost pairs were the same in both
sessions. Namely, we considered the pairs (0,0), (40,0) and (40,40). However, to
control for order effects, the sequence in the second session was modified to (40,40),
(0,0) and (40,0). Subjects were paid a $5 show-up fee and the sum of their earnings
over all 45 paid matches, in cash, in private, immediately following the session at
the exchange rate of 160 points = $1.00. Sessions averaged one hour and a half in
length, and subject earnings averaged $21.
30
9.2 Experiment 2
The experimental game 2 closely followed the Model III setting described in section
8. We also ran two sessions of this experiment in which subjects formed 3 groups
of 5 and 2 groups of 7 respectively. At the beginning of the session, groups were
formed and each subject in a group was randomly assigned a role as either A, B or
C. In groups of 5, two players were assigned Role A and two players were assigned
Role B. In groups of 7, three players were assigned Role A and three players were
assigned Role B. In either case, one player was always assigned Role C. The groups
and roles remained fixed for the entire session. In each match, two numbers were
then drawn randomly from a uniform distribution between 0 and 100. One of these
numbers, called state A, was disclosed to all the players with role A. The second
number, called state B, was disclosed to all the players with role B. All players in
Roles A and B had then to decide independently and simultaneously whether to
disclose the corresponding state to agent C or not. There were no costs associated
with withholding information in this experiment. The remaining player C could
then view the decision of players in roles A and B. More precisely, by clicking
on a button hiding the information relative to a player with role A, state A was
revealed to C if that player decided to transmit, and the computer reported that
the state was “unknown” if that player decided to withhold. That is, whenever the
state was reported unknown, C could infer that the player decided to withhold the
information. The same applied to state B and players with Role B. Revealing the
decisions of a player in role A or B was costly to C but yielded a benefit to that
player. The costs varied as we will detail below. Player C had to take two actions
consisting in choosing two numbers between 0 and 100. The payoffs, denominated
in points of subjects in roles A, B and C were respectively:
pi
A
= 50+z
A
?z
B
+b
A
, pi
B
= 50+z
B
?z
A
+b
B
, pi
C
= 120?
(z
A
??
A
)
2
40
?
(z
B
??
B
)
2
40
?k
where ?
i
is state i, z
i
is the action taken by C regarding state i, b
i
is a variable that
takes value 0 if C did not view that player’s decision and 20 if he did, and k is the
total cost paid by C for viewing the decisions of the A and B players. According to
these payoffs, subjects with role A want C to take a high action z
A
and a low action
z
B
whereas subjects in role B want the opposite, although with their transmission
/ withholding decision they can only influence the action regarding their own state.
Moreover, each subject with role A or B wants C to view his own decision in
order to obtain the extra payoff. This captures reputation effects. Finally and as
in experiment 1, the quadratic scoring rule implied that subjects in role C should
take the action closest to their expected belief of the state. Again, this was clearly
31
explained in the instructions. Unfortunately and as we will develop below, some
subjects in sessions 3 and 4 did not seem to comprehend that aspect of the game.
In both sessions, subjects participated in 40 paid matches, with states randomly
drawn at the beginning of each match. The design included two blocks of twenty
matches, where the cost for C of viewing the decisions of A and B were identical
within blocks and different across blocks. In the session with groups of five partici-
pants, in the first block, viewing the decision of one A player had cost 5 and viewing
the decision of a second A player had cost 30. Viewing the decision of one B player
had cost 10, and viewing the decision of a second B player had cost 50. The costs
for viewing decisions by A and B players were reversed in the second block. In the
session with groups of seven participants, Role C could reveal the decision of at
most two players with Role A and at most two players with Role B. The costs were
the same as in the session with groups of five participants. Sessions averaged one
hour and a half in length. Subjects were paid a $5 show-up fee and the sum of their
earnings over all 40 paid matches, and their earnings averaged $20.
10 Results of experiment 1
10.1 Aggregate analysis
We first conducted an aggregate analysis of the experimental data. Our objective
was to determine whether actual decisions were close to our theoretical predictions
for each of the roles and for each pair of costs. From now on, the cost pairs (c
A
,c
B
)
we used in the experiments, namely (0,0), (40,0) and (40,40), will be denoted LL,
HL and HH where L stands for ‘low’ and H for ‘high’. Table 2 summarizes the
theoretical predictions using the analytical expression derived in Example 2. In each
case, subjects in Role A should withhold low values of the state ? while subjects in
Role B should withhold high values of ?. The optimal decision of C is to choose an
action equal to the true state when it has been transmitted by both A and B. When
the state is not transmitted, C should report the expected value of ? conditional on
observing no transmission.
Not surprisingly, subjects are supposed to withhold less frequently when their
cost increases. In our case, A’s cutoff decreases as we move from LL to HLand B’s
cutoff increases as we move from HL to HH. Perhaps more subtly and as already
discussed in the theory section, costs are strategic complements: an individual is
less likely to withhold information as the cost of the other individual increases. In
our case, A’s cutoff decreases as we move from HL to HH and B’s cutoff increases
as we move from LL to HL.
32
LL HL HH
A withholds ? < 50 ? < 18 ? < 10
B withholds ? > 50 ? > 58 ? > 90
C’s action if uninformed 50 58 50
Table 2: Theoretical Predictions
Figures 1, 2 and 3 represent the distributions of the behavior of players in Roles
A and B for each pair of costs. Due to the relatively small number of observations,
we grouped the states in bins of 10, that is, [0-10], [11,20], [21,30], etc. For each bin,
we computed the proportion of times players in each role withheld the information.
The figures also report the total number of observations in each bin. We can see
that the decisions are qualitatively consistent with the theoretical predictions. For
instance in the LL configuration, Nash equilibrium theory predicts that subjects
in Role A would withhold information with probability 1 if the state was below
50 and with probability 0 if the state was above 50. Predictions in Role B were
reversed. Naturally, the empirical behavior does not exhibit such extreme behavior
of either always or never withholding. However, we still notice a sharp decline near
the equilibrium threshold 50. A similar decline is observed in the other two cost
configurations. To formally test for differences between theoretical predictions and
empirical behavior, we ran McNemar’s ?
2
tests to compare the actual decision to
“Withhold” or “Transmit” with the Nash equilibrium in each trial for each Role
and under each cost configuration. Differences were not statistically significant for
LL under either role. For HL, differences were statistically significant at p<0.01
for Role A and at p<0.05 for Role B. Finally, for HH the differences were again
statistically significant at p<0.01 for Role A and significant at p<0.1 for Role B.
Table 3 presents a different look at the same data. It summarizes the number
of instances where only A, only B, both A and B and neither A nor B transmitted
information. It also compares these observations with the theoretical predictions.
LL HL HH
theory emp. theory emp. theory emp.
Only A withholds 61 44 15 20 15 26
Only B withholds 59 46 50 53 13 18
Both A and B withhold 0 18 0601
Both A and B transmit 0 12 55 41 92 75
Table 3: Withholding strategies
33
Again, the table suggests that empirical behavior matches reasonably well the
theoretical predictions. Perhaps the most noticeable difference is that, contrary to
the theoretical predictions, both agents sometimes choose simultaneously to with-
hold information. However, this occurs in less than 7% of the observations.
We then studied the effect of a change in the costs of withholding on the decision
to withhold. To analyze the effect of the cost faced by a player on his own behavior,
we compared the decision of players with Role A under LL with their decisions under
HL and the decision of players with Role B under HL with their decisions under
HH. We used a two-sample Wilcoxon test to test for the equality of the distributions
of behavior and found that in both cases the distributions were significantly different
at p<0.1. To analyze the more subtle effect of the cost of the rival, we compared
the decision of players with Role A under HLwith their decisions under HH and the
decision of players with Role B under LL with their decisions under HL. Contrary
to the theoretical predictions, we found no statistical difference between the two
distributions in either case.
To complete the analysis, we ran a Probit regression of the decision of players
in Roles A and B as a function of the state and the cost parameters. The results
are reported in Table 4. For each role, the player’s own cost of withholding had a
negative and significant effect. Also, subjects in Role A withheld significantly less
often the higher the state whereas subjects in Role B withheld significantly more
often the higher the state. This is consistent with the results we already reported.
The indirect effect of the rival’s cost on a player’s probability of withholding had
the correct (negative) sign but was not statistically significant, again in line with
the results of the Wilcoxon test.
8
Result 1 The decision of subjects in Roles A and B to withhold information is
remarkably close to the theory predictions, with the state being rarely revealed in
the absence of a cost of withholding. Subjects’ reaction to an increase in their own
cost is also remarkably close to the theoretical predictions. However and contrary to
equilibrium theory, subjects do not react to an increase in the rival’s cost.
We started the study of the behavior of agents in role C by checking whether
they choose a decision equal to the state whenever it was transmitted. They over-
whelmingly do, as we found only one mistake by one player in the first round of a
session. Naturally, the more interesting analysis consists in studying the behavior
8
Instead of a “reduced-form” Probit estimation, it could be also interesting to build a stochastic
choice model that could then be structurally estimated (as for example in Quantal Response
Equilibrium (McKelvey and Palfrey, 1995)).
34
A witholds B withholds
State -0.0401*** 0.0415***
(0.00636) (0.00619)
Cost of A -0.0291*** -0.00613
(0.00778) (0.00541)
Cost of B -0.00335 -0.0387***
(0.00415) (0.00723)
Constant 2.073*** -1.925***
(0.356) (0.371)
N 360 360
Pseudo R
2
0.411 0.437
Clustered standard errors in parentheses
*** p<0.01
Table 4: Probit analysis
when C is not informed about the state. Table 5 reports some basic statistics in
this case.
LL HL HH
# obs. 108 79 45
Mean 54.37 55.83 55.44
Std. Dev. 16.85 19.05 20.77
Table 5: Action by Role C
Remember from Table 2 that C should choose actions 50, 58 and 50 under
LL, HL and HH respectively. The empirical decisions are, on average, relatively
‘close’ to each other and to the theoretical prediction. To analyze differences more
rigorously, we used a Wilcoxon test to test for the equality of the actual decisions and
the theoretical prediction. For LL and HH the hypothesis was rejected at p<0.05
and p<0.10 respectively, suggestion that actions by C are higher than predicted.
The same test showed that under HL differences between actual choices and Nash
theory are not statistically significant. It is also interesting to determine whether
35
empirical choices are different for the different cost pairs. Again, we performed a
series of Wilcoxon tests and found that differences in the distribution of behavior
between LL and HH and between HL and HH are not statistically significant but
that differences between LL and HL are significant at p<0.10.
Figure 4 depicts the cumulative distribution function of the decision made by
subjects with Role C for each pair of costs. Notice that for LL there is a substantial
fraction of players choosing exactly 50. This is also the case for HH, although the
proportion of observations in [51-80] is larger in that case (around 25%). Finally, it
is interesting to notice that in HL, the two modal choices are 50 and 60, although
the dispersion of choices is substantially larger. The result can be summarized as
follows.
Result 2 Subjects in Role C play on average according to theory when they do not
know the state. However, there is substantial dispersion in their behavior.
Overall, the aggregate analysis suggests that behavior is reasonably in line with
our predictions, which implies that when two medias with opposite objectives can
garble information which is contrary to their interests, they will do it. This results
in very little information transmission in equilibrium. For the case of Roles A and
B, subjects understood the simpler strategic aspects of the game (the effect of
their cost on the decision to transmit information). Nevertheless, their choice does
not reflect variations in the cost of the rival, which is a more subtle consideration.
Subjects in Role C make decisions that are also close to Nash theory. A fraction of
players also seem to realize that in the asymmetric case (high cost for A and low
cost for B) withholding is more likely to come from B and react by choosing higher
actions. However, the aggregate differences are small. Also, the behavior is more
erratic which translates into a larger dispersion of choices. In general, we notice an
attempt by C to base the decision on the information that is observed. If players
C were neglecting the fact that A and B act strategically, their action would be to
choose 50 in all scenarii.
10.2 Individual analysis
Our next step of the analysis consists in looking at the data at the individual level.
First, we determine whether subjects employ stable cutpoints strategies. Indeed, for
each state subjects in roles A and B need to choose whether to withhold or transmit
the state. It seems natural that if a subject in role A transmits state x, she should
transmit all states that are more favorable than x (that is, all x
prime
>x) and if she
withholds state y, she should also withhold all states that are less favorable than y
36
(that is, all y
prime
<y). The symmetric reasoning should apply to subjects in role B.
We look at the behavior of each individual in each role and for each pair of costs
separately and determine whether there is a stable cutpoint (optimal or not) that
could rationalize their choices. The results are presented in Table 6.
session 1 2
costs LL HL HH LL HL HH
Role A 8 11 12 11 11 11
Role B 7 11 12 11 10 11
number of subjects per role and cost pair is 12
Table 6: Individuals using cutpoint strategies
In the vast majority of the cases (126 out of 144) subjects use stable cutoff
strategies. In 9 out of the 12 treatments, either 11 or all 12 out of 12 subjects use a
cutpoint strategy. This is not all that surprising since the aggregate analysis already
showed that behavior in roles A and B is quite close to the theoretical predictions.
Some mistakes occur simply because subjects play many matches (45) and they
may sometimes misread whether they are currently playing under role A or B.
9
The
exception is session 1 under cost LL, where 4 out of 12 subjects in role A and 5 out
of 12 subjects in role B do not play according to a cutpoint strategy. A possible
explanation is that LL corresponds to the first treatment played by subjects in that
session, and that individuals are still learning how to play the game.
A more stringent test consists in determining whether subjects who do use a
cutpoint strategy apply the optimal one. Table 7 presents the number of individuals
per treatment whose behavior can be rationalized by the use of a cutpoint strategy
which is within 5 units of the optimal one.
10
By definition, only those individuals
using cutpoints strategies as defined in Table 6 are candidates for optimal cutpoints.
Overall in three-quarters of the cases where subjects use cutpoint strategies, the
cutpoints are “approximately optimal” (95 out of 126). This also corresponds to
two-thirds of all cases (95 out of 144), which reinforces our previous conclusion that
subjects play this game rather well.
9
For example, we have one case of an individual in Role B who always plays according to the
theory except for one observations where he/she transmits when the state is 81. It is likely that
the subject believed he/she was in Role A.
10
So, for example, a subject with role A in HH whose choices are consistent with a strategy of
withholding when ? ? 45 and transmitting when ? ? 46 will be considered as using an optimal
cutpoint strategy. We include some degree of freedom (±5 units) to allow for minor deviations.
37
session 1 2
costs LL HL HH LL HL HH
Role A 7 8 10 8 7 6
Role B 7 9 10 9 6 8
number of subjects per role and cost pair is 12
Table 7: Individuals using “approximately optimal” cutpoint strategies
In Figure 5 we look at each individual (ordered by their ID number) and de-
termine the number of mistakes under roles A or B during the entire experiment,
that is, for all three costs pairs. Subjects play on average 30 times in those roles
(10 times under each cost pair). According to this figure, half the subjects make
3 mistakes or less (about 10% of the time or less) during the entire session, with
two subjects not making any mistake at all and no subject making more than 10
mistakes overall. The result of the individual analysis is summarized as follows.
Result 3 Most players withhold information using a rational and consistent cut-
point strategy. Half the subjects play extremely close to the theory and less than
20% exhibit significant departures. Most departures occur in the first matches of the
experiment.
Finally, there is an interesting relation between this experiment and some previ-
ous literature. Brocas, Carrillo and Palfrey (2010) show that agents with opposing
interests strategically collect information to influence the behavior of decision mak-
ers. In particular, if the current belief is against the interests of one agent, she will
actively search for information in the hope that it will contradict current evidence.
The present paper shows that conditional on having the information, agents with
opposing interests will also strategically choose whether to convey it or not to an
unbiased third party in order to influence her choice. Both dimensions (strategic
collection and strategic revelation) affect final decisions. Subjects in the laboratory
experiments realize to a large extent the strategic aspects of this process.
11 Results of experiment 2
Experiment 2 consisted of two sessions (sessions 3 and 4). In session 3 we collected
data on 3 groups of 5 players (groups 1, 2 and 3) whereas in session 4 we collected
data on two groups of 7 players (groups 4 and 5). A first pass at the data reveals
that the players in Role C in groups 1 and 5 made a large number of trivial mistakes.
38
In particular, these two players typically incurred the cost of viewing the decision
of players in roles A and B. Then, they chose an action different from the state
in 40% and 98% of the observations respectively. Given that viewing is costly, the
C player in group 5 for example ended up obtaining a negative payoff.
11
In our
view, these two subjects did not understand the rules of the experiment and may
have completed the quiz by selecting answers randomly until they were correct. In
any case, there was very little information to extract from their behavior. It is also
difficult to infer anything from the behavior of other players in those groups, since
they could clearly see the erratic nature of their partner’s behavior. We therefore
decided to remove the observations obtained for these two groups. This leaves us
with less data than ideal: two groups of five players (groups 2 and 3) and one group
of seven players (group 4). In those groups, we counted only 2 mistakes by C in the
189 observations where the state was revealed.
12
Remember there are two possible cost configurations vis-`a-vis the A and B play-
ers. In the first one, viewing the decision of one agent costs 5 points to the C player
and viewing the decision of a second agent costs 30 points to the C player. We call
this configuration “low cost”. In the second one, the costs are 10 and 50 rather than
5 and 30.
13
We call this configuration “high cost”. In the first 20 rounds of the
experiment, C faced a “low cost” configuration with respect to state A and the A
agents and a “high cost” configuration with respect to state B and the B agents. In
the last 20 rounds, the cost configurations were reversed.
Note that when C does not attempt to view the decision of A or B players, he
should choose action a = E[?] = 50. Given the payoff function considered in the
experiment, the expected loss of choosing that strategy is:
14
?
integraldisplay
100
0
(s?50)
2
40
1
100
ds = ?20.83
This loss should be compared to the cost of viewing an agent’s decision (5 in
the low cost configuration and 10 in the high cost). This means that C should
11
We did not subtract this payoff and paid him the full show-up fee of $5. Notice that by using
a suboptimal and very conservative strategy of never viewing any decision and choosing 50 all the
time, that subject would have earned approximately $18 (plus show-up fee). For comparison, the
other C player in the session (group 4) earned $25.50 (plus show up fee).
12
This extremely low proportion of mistakes is consistent with the behavior in sessions 1 and 2
of experiment 1.
13
Recall that the groups of 5 and 7 were identical in that respect: the decision of the third agent
in the group of seven could never be observed.
14
Recall that C players get a fixed 120 points in each match to which the costs of actions and
viewing decisions are subtracted.
39
view the decision of one A or B player if he anticipates that they will transmit the
information with probability greater than 5/20.83 similarequal 0.24 and 10/20.83 similarequal 0.48 in the
low cost and high cost configurations respectively. Since A and B should compete `a
la Bertrand in the information transmission game and always reveal the state, it is
optimal for C to view the decision of one agent under either configuration. Moreover
if, out of equilibrium, C learns that the agent has withheld the information, then
he should never look at a second agent. Indeed, the maximum possible gain (if that
agent reveals with probability 1) is 20.83 and the cost is either 30 or 50.
11.1 Aggregate analysis
Despite the relatively small number of subjects, we can draw interesting conclu-
sions regarding the three important decisions in the experiment: (i) the decision to
transmit or withhold by A and B; (ii) the decision of C to view the information
transmitted (if any); and (iii) the action of C when the state remains unknown.
Figures 6-9 represent the distribution of the probability of withholding by players
pooling roles A and B but separating by group size (5 or 7) and cost configuration
(low or high). Contrary to the theoretical predictions, players withhold information
a substantial fraction of the time for all values of the state (40.6% in groups of 5 and
17.9% in the group of 7). We also observe a declining probability of withholding as
the state increases, although not as sharply as one would expect.
15
We ran a series
of McNemar’s ?
2
test by groups, role and cost configurations and they revealed
that the decision was statistically different from the theoretical prediction of never
withholding. We also ran a Wilcoxon test to test for the equality in the probability
of withholding between cost structures and we found no statistical difference.
Most of the time player C viewed at least one of the agent’s decision about
each state. Table 8 shows how many times player C viewed 0, 1 and 2 decisions
for each group. In the overwhelming majority of cases (231 out of 240) player C
viewed exactly one decision. Also, whenever player C viewed two decisions, the
information was either not revealed or revealed by at most one player.
16
This is in
strong accordance to the theoretical predictions where viewing one (but not two)
decisions is optimal if player C thinks there is a reasonable chance that the player
has transmitted it.
15
For example, for the groups of 5 with high cost, in 5 out of 26 observations subjects withhold
information when the state is above 80. Given such favorable state and no cost of transmitting,
one would think that subjects should be eager to let player C know about these “good news”.
16
Our software did not record the order of decisions viewed and it is not possible to see directly
whether C opened a second box after a transmission or a no transmission, but in line with a
rational choice, we strongly suspect that it is the latter.
40
Decisions viewed
012
Group 2 (5 players) 1 78 1
Group 3 (5 players) 0 79 1
Group 4 (7 players) 2 74 4
Table 8: Distribution of clicks
Player C obtained information frequently. There were only 5 out of 80 obser-
vations in the group of 7 (6.3%) and 46 out of 160 observations in the groups of 5
(28.8%) where C did not learn the state. These include 3 observations where player
C chose not to view any decision and 48 observations where he did view at least
one. When the state remained unknown, the reported actions averaged 10 in the
group of 7 (although the number of observations is very small). We summarize the
reports for the groups of 5 players in Table 9. Players tended to report higher values
for state A independently of the cost.
First 20 rounds State A State B
Mean 42.55 34.26
Std. Dev. 14.62 25.58
Last 20 rounds State A State B
Mean 48.5 38.13
Std. Dev. 18.28 27.11
Table 9: Actions by C when uninformed (groups of 5)
Interestingly, C consistently chose actions below the average state. Notice that
50 is the optimal choice if C decides not to view any decision. However, after
viewing a decision and learning that player A or B has (out of equilibrium) chosen
to withhold the state, he realizes that this is most likely to have occurred because
the state is low. It is therefore natural to reduce the ex-post belief of the state.
Notice also that subjects are less likely to withhold in groups of 7 than in groups
of 5. Therefore, no information in the former case is a stronger indication of a low
state than in the latter case. This would explain the substantially lower choice of
action under no information in the group of 7 (around 10) than in the groups of 5
(around 40). However, we do not want to stress this result excessively given that
it is based on a very small sample. The results of the aggregate analysis can be
summarized as follows.
Result 4 A and B players withhold information more often than predicted by theory
41
(40.6% in groups of 5 and 17.9% in the group of 7). C players view almost invariably
one decision as predicted by theory and often become informed (71% in groups of
5 and 94% in the group of 7). They realize that when information is withheld, the
state is likely to be low and choose low actions (around 40 in groups of 5 and 10 in
the group of 7).
11.2 Dynamic effects and reputation
An important aspect of our design is reputation. Players remain in the same groups
and can learn from previous interactions. Our next step is to study the dynamics
of the behavior. The first indication that reputation plays an important role is
the fact that the proportion of instances where C viewed one decision and remained
uninformed (28.8% and 6.3% in groups of 5 and 7 respectively) is significantly smaller
than the overall probability of withholding by players A and B (40.6% and 17.9%
in groups of 5 and 7 respectively). In other words, C players seem to learn which
players are most likely to transmit their information and exploit that circumstance.
Interestingly, C generally does not view twice in a row the decision of the same
player if the state is not transmitted the first time. To see this, we counted the num-
ber of times C viewed a player who withheld information in match t and compared
it to the number of times C view the decision of the same player in match t+1. In
groups of 5, C continued to view the same player in 35% of the cases, and in the
group of 7 only in 14% of the cases. Table 10 shows the results.
# Decisions withheld at t # view same player at t +1
Groups of 5 45 16
Group of 7 7 1
Table 10: View same player when state is withheld.
Along the same lines, C does not switch to view the decision of a different player
when the state is transmitted to him. We counted the number of times player C
viewed a player who transmitted information in match t and compared it to the
number of times C switched to a different player in match t+1. C switched in 18%
and 6% of the cases in the groups of 5 and 7 respectively. The behavior of C in
the group of 7 shows a stronger level of rationality since he has more options for
deviations and yet decides to switch less frequently. The results are summarized in
Table 11.
42
# decisions transmitted at t # switch player at t +1
Groups of 5 112 20
Group of 7 73 5
Table 11: Switch players when state is transmitted.
A more detailed description of the dynamics can be found in Figures 10-15. For
each state (A or B) and each group (2, 3 or 4) it plots which player the subject
in role C chose to view (labeled 1 or 2 in the groups of 5 and 1, 2 or 3 in the
group of 7). It also shows whether the decision of that player was to transmit (blue
diamond) or withhold (red square) the information. The main conclusions can be
summarized as follows. First, except for a few observations, the strategy of C is to
view one player for each state and keep viewing that same player as long as the state
is transmitted (the diamonds). When it is not (a square), C switches to another
potential provider of information. Rarely C switches without motive or stays with
a player who withholds. Second, players in Roles A and B realize C is playing
the strategy we just described. A player who knows C obtains information from
him tends to continue transmitting information. As a result, there are remarkably
long streaks of mutual understanding between C and one of the A or B players,
where the former keeps viewing the same player and the latter retains attention
by revealing his information (for example, in the group of 7, the streak lasts for
32 and 30 matches for state A and B respectively). Third, in the majority of the
cases, the behavior of players is consistent with the theoretical prediction. Player C
almost invariably views the decision of exactly one player per state. If that player
withholds information, he moves to the next match without viewing the decision of a
second one. Also, the player who anticipates to be viewed transmits his information.
However, we know from the analysis of the probability of withholding that players
tend to withhold relatively often. In fact, many players who know that C is not
observing their decision choose to withhold. For example, player B
2
in group 2
withheld 15 times after round 24, when C obtained information from B
1
. Player
A
2
in group 3 withheld 19 times after round 15, when C obtained information from
A
1
. This behavior, however, is not shared by all players. For example, in group
4, C obtained information from A
1
after round 9. In that group, A
3
withheld 15
times after that round whereas A
2
withheld 0 times. The withholding pattern of the
“ignored” subject may be the result of frustration, whereas the transmission pattern
may occur in the hope of a future switch. The result regarding reputation effects
can be summarized as follows.
43
Result 5 Subjects develop strong reputations: C players stick to agents who trans-
mit information and A and B players transmit information to keep their partnership
with C.
11.3 Group size as a disciplining mechanism
Last, a major motive to run sessions with groups of 5 and 7 players was to determine
the impact of group size on behavior. From Figures 6-9, we see that the probability of
withholding is generally smaller in the larger group (40.6% in groups of 5 and 17.9%
in the group of 7 pooling high and low cost together). A two-sample Wilcoxon test
revealed statistically significant differences at p<0.1 in the low cost configuration
and at p<0.01 in the high cost configuration. It suggests that players in Roles A
and B understood that it is relatively more difficult to coordinate their decisions on
“withhold” the stronger the competition within viewpoints, that is, the higher the
number of players with identical preferences and information. Also, if a C player
stops “trusting” a partner, he has more alternatives to choose from, so it is less likely
that he will come back. Not surprisingly, we also get that, in equilibrium, player C
in groups of 5 remains uninformed about the state substantially more often than in
the group of 7 (28.8% v. 6.3%). This is due to the differences in the withholding
behavior mentioned above, but also to the fact that player C in the group of 7 is
more systematic about switching partners who withhold information and keeping
partners who transmit it than player C in the groups of 5.
From Figures 10-15, we can also see that the behavior converges to the theoretical
prediction more rapidly in the group of 7 than in the groups of 5. Furthermore, the
streaks during which the predicted outcome is obtained (C views one player who
transmits information) are much longer in the larger group. Table 12 reports the
round after which player C always views exactly one player per state and obtains
always the information. This is the outcome predicted by the theory. We can see that
there is no or a very late convergence in groups of 5, whereas convergence is fast in the
group of 7. Perhaps more importantly, Table 13 reports the longest streak of matches
where C views exactly one player per state and obtains always the information.
Again, the streaks are much shorter in the groups of 5. After a few periods of playing
at equilibrium, the player in Role A or B who has been the source of information
starts deviating. This is generally followed by a switch to another potential provider
of information. A possible explanation for these differences between groups of 5 and
group of 7 is the fact that with 3 players in the same role, C has two alternatives
in order to discipline the behavior of the player whose information he is currently
viewing. Therefore, even if one of them is playing out of equilibrium (withholding)
44
there is still another option. This is indeed what seems to be happening in group
4. For the last 30 matches of the game, Player C stays with A
1
and B
3
(who
always transmit). In the meantime, A
3
and B
1
withhold information 15 and 7
times. However, A
2
and B
2
withhold 0 and 1 time respectively. In other words,
if A
1
or B
3
were to deviate, C could still find at least one other player willing to
transmit.
State A State B
Group 2 (5 players) 40 40
Group 3 (5 players) 30 40
Group 4 (7 players) 9 11
Table 12: Match at which behavior converges to the theoretical predictions
State A State B
Group 2 (5 players) 4 13
Group 3 (5 players) 14 13
Group 4 (7 players) 32 30
Table 13: Length of the longer streak consistent with the theoretical predictions
Taken together, these results suggest that, even tough players deviate sometimes
from the theoretical predictions, there is more discipline in larger groups. Given the
small number of observations, it is not possible to draw finer conclusions. Neverthe-
less, these results are promising: increasing competition within viewpoints (even if
it is just from two to three) should promote transmission of information.
Result 6 The level of competition within viewpoints matters: A and B transmit
more information, C learns the state more often and longer partnerships are formed
in the group of 7 than in the groups of 5.
Overall, players do understand the reputation effect: playerC exploits reputation
to extract information, and players A and B transmit information to generate a high
reputation. However, in the presence of costs of acquiring information, a player who
transmits does not benefit from reputation if player C never check his decisions. In
other words, costs induce inertia and it is extremely important to “capture” C as
early as possible. It is therefore necessary to have several players in each Role to
45
increase the probability of transmission, even though only one of them benefits from
the reputation effect in equilibrium.
Notice also that we have focused on one representative voter or media consumer
(player C). If we considered many consumers, it could be the case that some would
develop strong reputations with one A player and others with a different A player.
In equilibrium, every media would reveal information to keep their base and try to
“steal” consumers from other medias. It could be interesting to study this variant
in the laboratory.
12 Concluding remarks and future research
This paper has analyzed the incentives of media outlets with preferences over policy
outcomes to withhold information that goes against their interests. Building on
Blackwell’s theorem on the comparison of information structures Blackwell, (1953),
we have argued that consumer’s welfare increases if the media outlets provide more
information in a mathematically precise sense.
We have then provided three theoretical benchmarks. In the first one, we study
a media with monopoly power over information (or, equivalently, two medias each
one with information about a different aspect of policies). We show that if the media
does not receive information with positive probability, then it can claim ignorance
in order to avoid reporting unfavorable evidence. In equilibrium and conditional
on receiving information, a media is more likely to claim ignorance the higher the
probability of not being informed. This result, which is reminiscent of Dye (1985),
suggests that information which is more difficult to obtain is more subject to manip-
ulation or, more precisely, to suppression. Although interesting, the setting ignores
strategic considerations in the incentives of different media sourcess to report news.
Our second benchmark explicitly incorporates competition between viewpoints for
information provision. We consider two medias with opposite preferences who al-
ways obtain the information and can decide to withhold it, possibly at a cost. We
assume that information reaches consumers only if both transmit it. The idea is that
even if one media wants to inform the consumer, the other can provide arguments
that introduce noise and garbles the signal. In that setting, we show that each media
has strong incentives not to transmit information which goes against its interests.
Therefore, in equilibrium, only “neutral” information (that is, information which is
not strongly in favor of the interests of one media and strongly against the interests
of the other) will be eventually transmitted. In the extreme case where garbling in-
formation is costless, no news will ever reach consumers. We find that as the cost of
information garbling increases, more information is transmitted, and for sufficiently
46
high costs all information is revealed. We can interpret these costs as “reputation
costs” that is if a media outlet gains a reputation for being uninformative then
consumers will punish it with a loss of audience and so revenues. Our third and
last benchmark deals with competition within viewpoints. We assume that several
medias with identical viewpoints can withhold or transmit information. Contrary to
the previous setting, withholding information is costless. Moreover, medias benefit
not only from transmitting biased information but also from consumers’ observing
their choice (for example, buying the newspaper or watching the TV channel). In
that situation there is a “Bertrand” type of competition: each media wants to be
observed by consumers so they all choose to reveal their information in equilibrium.
In other words, competition within viewpoints dramatically enhances information
revelation.
We have then tested the theory in controlled laboratory experiments. In Ex-
periment 1, we test the model of competition between viewpoints. Our subjects
play remarkably close to Nash equilibrium predictions. In particular, when the cost
of withholding information is nil, the subject with unfavorable information always
withholds it so that news rarely reach consumers. As the costs increase, information
withholding decreases. Finally, consumers realize that withholding is more likely by
medias with lower costs and choose their action accordingly. The only significant
departure of the empirical behavior relative to the theory is that subjects under-
react to changes in the cost of the rival. In Experiment 2, we test the model of
competition within viewpoints. In that case, deviations from theoretical predictions
are more significant. Nevertheless, the empirical behavior converges to the theoret-
ical predictions quicker when there is more competition. This benefits consumers
as the information is transmitted more often. This suggests that an increased num-
ber of medias generates discipline among outlets and promotes the dissemination of
information.
Future research should focus on three under-explored aspects of the analysis.
First, the relation of this paper with the existing literature is not fully explored.
It would be helpful to analyze more systematically the connections between each
of the three models and the existing theoretical and experimental papers on the
subject. Second, the connection between the three rationales for information with-
holding should be strengthened. We have emphasized the possibility of not having
any information as a possible “excuse” that a monopolist can use for not revealing
unfavorable information (model 1). Similarly, we have argued that competition be-
tween viewpoints generates diversity only if the cost of withholding is sufficiently
high (model 2). Finally, under competition within viewpoints, reputation can in-
duce unraveling of information if there are enough firms with similar preferences
47
and enough concern for attracting viewers (model 3). In practice, the three motives
are interrelated and the analysis would benefit from a closer look at the possible
interactions. Third, and most importantly, the results of the experiments are highly
informative but, nevertheless, in order to test their robustness, we would want to
have more observations. These considerations will be the object of future work.
48
13 References
1. Alterman, E. (2003). “What Liberal Media? The Truth About Bias and the
News.” Basic Books.
2. Alvarez, R. Michael. (1997). “Information and Elections,” U. of Michigan
Press.
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57
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B-1 
 
APENDIX B – INSTRUCTIONS 
 
FC -- EXPERIMENT 1 –  INSTRUCTIONS   – 01.16.201 
 
 Thank you for agreing to participate in this research experiment on group decision making. 
During the experiment we would like to have your undistracted atention.  Do not open other 
aplications on your computer, chat with other students, use your phone or headphones, etc.  
 
For your participation, you wil be paid in cash from a research grant, at the end of the 
experiment.  Diferent participants may earn diferent amounts.  What you earn depends partly on 
your decisions, partly on the decisions of others, and partly on chance. It is very important that you 
listen carefuly, and fuly understand the instructions. You wil be asked some review questions after 
the instructions, which you wil have to answer corectly before we can begin the experiment. 
 
If you have questions, don’t be shy about asking them. If you have a question, but you don’t 
ask it, you might make a mistake which could cost you money. 
  
The entire experiment wil take place through computer terminals. Al interaction betwen 
you and other participants wil take place through the computer interface. It is important that you not 
try to comunicate with other participants during the experiment, except acording to the rules 
described in the instructions. 
  
We wil start with a brief instruction period. During this instruction period, you wil be given 
a complete description of the experiment and wil be shown how to use the computer. At the end of 
the sesion, you wil be paid the sum of what you have earned in al matches. Everyone wil be paid 
in private and you are under no obligation to tel others how much you earned. Your earnings during 
the experiment are denominated in points. At the end of the experiment you wil be paid $1.0 for 
every _160_ points you have earned. 
 
 The experiment wil consist of several matches. In each match, you wil be grouped with two 
other participants in the experiment. Since there are __ participants in today’s sesion, there wil be 
__ groups of 3 in each match. You are not told the identity of the participants you are grouped with. 
Your payof depends only on your decision and the decisions of the two participants you are grouped 
with. What hapens in the other groups has no efect on your payof and vice versa. Your decisions 
are not revealed to participants in the other groups. 
 
 In each match, you wil have either Role A, Role B or Role C. Which Role (A, B, or C) you 
have is random in each match and is clearly displayed on the scren. The computer wil also draw one 
number betwen 0 and 10 and al numbers are equaly likely. This number is caled the state. 
 
What to do 
 
If you have Role A, the computer wil disclose the state to you. You wil then have to 
“Transmit” the state or “Withold” the state. If you chose to “Withold” the state, you wil pay a 
cost. If you chose to “Transmit” the state you wil not pay any cost. 
 
If you have Role B, the same options are ofered to you except that the cost if you chose to 
“Withold” the state may be diferent. Both costs wil be clearly displayed on your scren. Last, you 
wil not be able to se the decision of the participant in the other role when you make your decision. 
After chosing “Transmit” or “Withold”, you wil be instructed to wait. 
B-2 
 
 
If you have Role C, you wil be instructed to wait until the two other participants have each 
chosen to “Transmit” or “Withold” the state. Then, the computer wil display the cost of witholding 
for the participants with roles A and B. The computer wil also display the state if both roles A and B 
chose to “Transmit” the state. If at least one of them choses to “Withold” the state, the computer 
wil report that the state is “unknown”. In either case, you wil be prompted to select your action 
which consists of a number betwen 0 and 10. 
 
When the participant with role C has chosen the action, the computer displays the state and 
the action of role C. Each participant can also se the payof of al the participants in the group. 
 
When al groups have finished the match and have sen the results, we proced to the next 
match. For the next match, the computer randomly reasigns al participants to new groups. In each 
group, the computer asigns new roles, and randomly selects a new state betwen 0 and 10. The new 
asignments do not depend in any way on the past decisions of any participant including you and are 
done completely randomly by the computer. The asignments are independent acros groups, acros 
participants, and acros matches. This next match then folows the same rules as the previous match. 
 
How much you get 
 
If your role is A, your payof is the action selected by C minus the cost if you witheld the 
state. Therefore, A wants C to chose an action as high as posible. 
 
If your role is B, your payof is 10 minus the action selected by C minus the cost if you 
witheld the state. Therefore, B wants C to chose an action as low as posible. 
 
If you have Role C, your payof depends on both the state and the action. It is equal to: 
 
100 - (state - action)
2
 / 40 
 
Note that you maximize your earnings if you chose an action that equals your expectation 
regarding the state. To se this, supose you think there is 50% chance the state is 20 and 50% chance 
the state is 40. The amount you earn in expectation is: 
 
100 - 0.5(20 - action)
2
 / 40 - 0.50 (40 - action)
2
 / 40. 
 
Therefore if you chose action 20 or 40, your payof is 95 
Instead, if you chose 30 (that is, 20*0.5 + 40*0.5), your payof is 97.5. 
 
Finaly, if you know the state for sure, then you should chose your action equal to the state and 
obtain a payof of 10 for sure. 
 
There wil be one practice match. The points acumulated in this match do not count towards 
your final dolar earnings. The practice match is similar to the matches in the experiment. 
 
Before the practice match, we wil present the game using screnshots. It is important that 
you understand this information. If you have a question during this presentation, raise your hand and 
we wil answer you. 
B-3 
 
 
Display 1. Sample screnshot for roles A and B 
 
If you have either Role A or Role B, you wil se a scren similar to this: 
 
Your Role is displayed at the top of the scren. In that example, you have Role A. In that 
match, the state is 57. Your cost of witholding the state is 40 and the cost of witholding of the 
participant with role B is 0. If you want to Transmit, you have to click the “Transmit” buton. If you 
want to “Withold”, you have to click the “Withold” buton. 
 
Display 2. Sample screnshot for role C 
 
If you have Role C, you wil se a scren similar to this after A and B have made their choices: 
 
The costs of witholding for both roles A and B are clearly displayed. In that example, they 
are 40 and 0 respectively. The state is unknown in that example, which means that either role A or 
role B or both A and B have chosen to “withold” the state. You must chose your action by entering 
a number betwen 0 and 10 in the box and click “Submit”. 
 
B-4 
 
Display 3. Sample screnshot of the last scren 
 
This is the last scren you se in the match. 
 
 
Participants in al thre roles A, B and C se the exact same scren, except for the top line 
that displays your role and the botom history lines. In that example, the state was 63 and C selected 
action 8. The participant with Role A obtained 48 points, the participant with Role B obtained 12 
points and the participant with Role C obtained 84.38 points. These payofs corespond to a diferent 
match than the one in displays 1 and 2 and it is presented only for ilustration. 
 
At the botom of the scren, the history of previous matches is displayed. For each match, the 
scren shows the state, the decision of roles A and B (transmit or withold) and the action of role C 
(number betwen 0 and 10). It also shows your own role and the payof you obtained. To reach the 
next match, you ned to click “Continue”. 
 
Recap 
 Here is a brief recap of the important things you wil se, and how they afect your payofs: 
 
(1) Roles A and B know the state. Each choses whether to “Transmit” or to “Withold” the 
state. The decisions to “Withold” have costs for A and for B which are displayed. 
(2) Role C observes the state only if BOTH Roles A and B decided to “Transmit”.  Role C 
observes “state is unknown” if at least one of them choses to “Withold” the state. 
(3) The payof for A is the action of C minus the cost if A witheld the state. The payof for B is 
10 minus the action of C minus the cost if B witheld the state. 
(4) The payof of C depends on the state and his own action. It is maximized by reporting the 
expected value of the state based on the information observed. 
 
Are there any questions?  
B-5 
 
[PAUSE to answer questions] 
 
------------------------------------------------------------------ 
 
We wil now begin the Practice sesion and go through 1 practice match to familiarize you 
with the computer interface and the procedures. During the practice match, please do not hit any 
keys until you are asked to, and when you enter information, please do exactly as asked. Remember, 
you are not paid for the practice match. At the end of the practice match you wil have to answer 
some review questions. Everyone must answer al the questions corectly before the experiment can 
begin. 
 
[AUTHENTICATE clients] 
 
Please double click on the icon on your desktop that says ____. When the computer 
prompts you for your name, type your First and Last name. Then click SUBMIT and wait for further 
instructions. 
 
[START game] 
 
You now se the first scren of the experiment on your computer. Raise your hand high if 
you do. Please do not hit any key. 
 
[PAUSE TO BE SURE EVERYONE HAS THE CORECT SCREN] 
 
At the top left of the scren you se your subject ID. Please record that on your record shet 
now. Some of you have Role A, some have Role B and some have Role C. If you have Role A or 
Role B, the scren loks similar to the screnshot in display 1. If you have Role C, you are instructed 
to wait. In both cases, at the botom of the scren you can se a history panel with al the information 
relevant for each match. 
 
 If you have Role A or Role B and your subject ID is even, click on the “Transmit” buton. 
Otherwise, click on the “Withold” buton. Note that it does not mater which one you chose since 
you wil not be paid for this match. 
 
If you have Role C, you should now se a scren similar to the screnshot in display 2. It 
displays the state if both roles A and B chose to “Transmit”. Otherwise it displays “the state is 
unknown”. If you have Role A or Role B, you are instructed to wait. 
 
If you have Role C, type the last two digits of your social security number. It does not mater 
which number you type since you wil not be paid for this match. 
 
You should now al se a scren similar to the one in display 3. It displays the state, the action 
of C and the payofs of al participants in your group. 
 
Now click “Continue”. The practice match is over. Please complete the review questions 
before we begin the paid sesion. Once you answer al the questions corectly, click submit. After al 
participants in your group have answered al questions corectly, the quiz wil disapear from your 
scren. Raise your hand if you have any question. 
 
[WAIT FOR EVERYONE TO FINISH THE QUIZ] 
 
B-6 
 
Are there any questions before we begin with the paid sesion? 
 
We wil now begin with the paid matches. If there are any problems or questions from this 
point on, raise your hand and an experimenter wil come and asist you. 
 
For the next matches the cost of witholding for Role A is __ and for Role B is __.  
 
[at the end of GAME __] 
 
For the next __ matches the cost of witholding for Role A is __ and for Role B is __. 
The rules of the match are the same as before. 
 
[at the end of GAME __] 
 
For the next __ matches the cost of witholding for Role A is __ and for Role B is __. 
The rules of the match are the same as before. 
 
[at the end of GAME __] 
 
This was the last match of the experiment. You wil be paid the payof you have acumulated 
in the __ paid matches. The payof apears on your scren. Please write this payof in your record 
shet and remember to CLICK OK after you are done. 
 
[CLICK ON WRITE OUTPUT] 
 
We wil now pay each of you in private in the next rom in the order of your Subject ID 
number. Remember you are under no obligation to reveal your earnings to the other participants. 
 
Please put the mouse behind the computer and do not use either the mouse or the keyboard. 
Please remain seated until we cal you to be paid. Do not converse with the other participants or use 
your cel phone. Thank you for your coperation. 
 
[CAL al the participants in sequence by their ID #] 
 
[Note to experimenter: use the “pay” file to cal and pay subjects] 
 
Could the person with ID number 1 go to the next rom to be paid? 
 
 
B-7 
 
RECORD SHET 
 
 
 
 
Subject ID:      ______ 
 
 
TOTAL EARNINGS:     $___ 
 
 
 
 
 
 
Name:____________   Date:____________ 
 
  Amount received:_______ 
 
Schol ID #:__________   Signature:___________ 
 
 
 
 
 
 
B-8 
 
FC – EXPERIMENT 2 (groups of 5) – INSTRUCTIONS  – 01.17.201 
 
 Thank you for agreing to participate in this research experiment on group decision making. 
During the experiment we would like to have your undistracted atention.  Do not open other 
aplications on your computer, chat with other students, use your phone or headphones, read, etc.  
 
For your participation, you wil be paid in cash from a research grant, at the end of the 
experiment.  Diferent participants may earn diferent amounts.  What you earn depends partly on 
your decisions, partly on the decisions of others, and partly on chance. It is very important that you 
listen carefuly, and fuly understand the instructions. You wil be asked some review questions after 
the instructions, which you wil have to answer corectly before we can begin the experiment. 
 
If you have questions, don’t be shy about asking them. If you have a question, but you don’t 
ask it, you might make a mistake which could cost you money. 
  
The entire experiment wil take place through computer terminals. Al interaction betwen 
you and other participants wil take place through the computer interface. It is important that you not 
try to comunicate with other participants during the experiment, except acording to the rules 
described in the instructions. 
  
We wil start with a brief instruction period. During this instruction period, you wil be given 
a complete description of the experiment and wil be shown how to use the computers. At the end of 
the sesion, you wil be paid the sum of what you have earned in al matches. Everyone wil be paid 
in private and you are under no obligation to tel others how much you earned. Your earnings during 
the experiment are denominated in points. At the end of the experiment you wil be paid $1.0 for 
every _160_ points you have earned. 
 
 At the begining of the experiment, you wil be grouped with four other participants. Since 
there are __ subjects in today’s sesion, there wil be __ groups of five. You are not told the 
identity of the participants you are grouped with. Your payof depends only on your decision and the 
decisions of the participants you are grouped with. What hapens in the other groups has no efect on 
your payof and vice versa. Your decisions are not revealed to participants in the other groups. 
 
 In each group, there wil be thre types of roles, Role A, Role B and Role C. There wil be 
two participants in Role A, caled A1, A2 participants, two participants in Role B, caled B1, B2 
participants and one participant in Role C, caled C participant. You wil have either role A, role B or 
role C. Which role you have is randomly selected at the begining of the experiment and is clearly 
displayed on the scren. You wil kep the same role and wil be in the same group with the same 
participants for the entire duration of the experiment. 
 
The experiment wil consist of several matches. In each match, the computer wil draw two 
numbers. Each of these numbers can be any number betwen 0 and 10 and al numbers are equaly 
likely. These numbers are caled state A and state B. 
 
What to do 
 
If your role is A1 or A2 (you are an A participant) the computer wil disclose state A to you 
but not state B. Similarly, if your role is B1 or B2 (you are a B participant) the computer wil disclose 
state B to you but not state A. Al A participants se the same state A, and al B participants se the 
same state B. You wil then have to chose whether to “Transmit” or “Withold” the state. You wil 
B-9 
 
not se the decision selected by any of the other A or B participants when you make your decision. 
You wil then be instructed to wait. 
 
If you are a C participant, you wil be instructed to wait until al A and B participants have 
each chosen an action (“Transmit” or “Withold”). Then, you wil se four butons that hide the 
decision of each A and B participant. 
 
You wil first have the posibility to view the decision of each A participant. If you click on 
one of the A butons (A1 or A2), the computer wil reveal state A if that A participant chose 
“Transmit” and state “unknown” if that A participant chose “Withold”. You can then view the 
decision of another A participant, and so on. Notice that if the two A participants decided to 
“Transmit” and you view their decisions, the same number is revealed to you, namely state A. It is 
entirely your decision to view none, one or two decisions of the A participants. If you chose to view 
the decision of one A participant, it is also your choice whether to view the decision of A1 or A2. 
Finaly, there are costs of viewing these decisions. When you decide to not view any more decisions 
of A participants, you must take action A, which consists in typing a number betwen 0 and 10. You 
then ned to click “Submit”. 
 
You wil then repeat the same steps regarding B participants. The only diference is that the 
costs of viewing the decisions of the B participants are diferent, as explained after. When you decide 
to not view any more decisions of B participants, you must take action B, which consists in typing a 
number betwen 0 and 10. You then ned to click “Submit”. 
 
When the C participant has made his decisions, the computer reveals the states A and B and 
displays the actions A and B selected by the C participant. Each participant can also se the payofs of 
al the participants in the group. 
 
When al groups have finished the match and have sen the results, we proced to the next 
match. For the next match, the computer randomly selects two new numbers betwen 0 and 10 
which corespond to the new states A and B. In the new match, you wil be in the same group with the 
same participants and you wil kep the same Role. Also, at the botom of the scren you wil se a 
History sumarizing what has hapened in the past matches of your group: which A and B 
participants chose to transmit and which ones chose to withold, which decisions of As and Bs the C 
participant chose to view, what were the states A and B and what were the actions A and B taken by 
the C participant. 
 
How much you get 
 
If you are an A participant, your payof is 50 plus the diference betwen action A and action 
B. Furthermore, if C viewed your decision, then you also get an extra 20 points. Therefore, you want 
C (i) to view your decision (for 20 points), (i) to chose an action A as high as posible, and (ii) to 
chose an action B as low as posible. 
 
If you are a B participant, your payof is 50 plus the diference betwen action B and action 
A. Furthermore, if C viewed your decision, then you also get an extra 20 points. Therefore, you want 
C (i) to view your decision (for 20 points), (i) to chose an action B as high as posible, and (ii) to 
chose an action A as low as posible. 
 
If you are a C participant, your payof depends on both states and on both actions, and it is 
decreased by the total cost of viewing decisions of A and B participants. It is equal to: 
 
B-10 
 
120 – (state A – action A)
2
 / 40 – ( state B – action B)
2
 / 40 – cost of viewing As and Bs 
decisions. 
 
Note that you maximize your earnings if you chose each action equal to the expected value 
of the coresponding state. To se this, supose for simplicity there is only state A, and supose there 
is 50% chance that state A is 20 and 50 % chance it is 40, the amount you earn in expectation is: 
 
120 – 0.5(20- action A)
2
 / 40 – 0.5(40- action A)
2 
 / 40 –cost of viewing As and Bs decisions 
 
Therefore if you chose action 20 or 40, your payof is 15 – cost of viewing As and Bs decisions. 
Instead, if you chose 30 (that is, 20*0.5 + 40*0.5), your payof is 17.5 – cost of viewing As and Bs 
decisions. Naturaly, if you know one of the states for sure, then you should chose the action for that 
state equal to the state. 
 
The cost of viewing the decisions of A and B participants are as folows. In the first part of the 
experiment, the first decision of an A participant you view costs _5_ points (it is the same cost for 
viewing the decisions of A1 and A2). The second decision of an A participant you view costs _30_ 
points. Similarly, the first decision of a B participant you view costs _10_ points, and the second 
decision of a B participant you view costs _50_ points. The costs in the second part of the experiment 
wil be reversed, and wil be clearly explained when we reach that stage.  
 
There wil be one practice match. The points acumulated in this match do not count towards 
your final dolar earnings. The practice match is similar to the matches in the experiment. 
 
Before the practice match, we wil present the game using screnshots. It is important that 
you understand this information. If you have a question during this presentation, raise your hand and 
we wil answer you. 
 
Display 1. Sample screnshot for A and B participants 
This scren is displayed to you if you are either an A or a B participant. The exact Role is displayed at 
the top of the scren. In that example, you are participant B1. 
 
  
In that match, state B is 85. You have to chose betwen “Transmit” or “Withold” the state. You 
simply ned to click the coresponding buton. 
B-11 
 
 
Display 2. First sample screnshot for C participant 
This scren is displayed to you if you have Role C and after al A and B participants have made their 
decisions. 
 
You have the posibility to view the decisions of A1 and A2. You must then enter a number in the 
box and click “Submit”. Notice that below those boxes are butons to view the decisions of B 
participants, but they are disabled at this point. 
 
Display 3. Second sample screnshot for C participant 
 
This scren is the second scren you se when you have Role C. Once you have submited your 
decision regarding state A, the butons to view the decisions of A participants are disabled. The 
number you submited is also visible but you canot change it anymore.  
 
In this example, you viewed the decision of A1 who transmited the state, so you learned that 
state A was 84. You also viewed the decision of A2 who chose to withold the information. Finaly, 
B-12 
 
you chose action 9. Note that this is an ilustration: the decisions and numbers only reflect a 
randomly generated behavior. 
 
Now, you have the posibility to view the decisions of B1 and B2. Last, you must enter a 
number in the box and click “Submit”. 
 
Display 4. Sample screnshot of the last scren 
 
This is the last scren you se in the match. Al participants se the exact same scren, except for the 
top line that displays only your role. 
 
 
The scren shows the states A and B, the actions A and B chosen by the C participant and the payofs 
of al participants in the group. To reach the next match, you ned to click “Continue”. 
 
Notice that at the botom of the scren, you can also se the history of previous matches. For each 
match, the scren shows the states A and B, the decision of each A and B participant, whether C 
viewed the decisions of each of the A and B participants, and the actions A and B chosen by C. This 
history scren is important as it tracks the past behavior of each participant. 
 
Recap 
 
 Here is a brief recap of the important things you wil se, and how they afect your payofs: 
 
(1) Roles A know state A and can chose to “Transmit” or “Withold” it to C. Similarly, Roles B 
know state B and can chose to “Transmit” or “Withold” it to C. 
(2) If C clicks on a participant’s buton, C wil learn the state if that participant chose “Transmit” 
and he wil se “unknown” if that participant chose “Withold”. Clicking on a participant’s 
buton is costly. 
(3) The payof of an A participant is 50 + action A – action B + 20 
 
if C views your decision. The 
payof of a B participant is 50 + action B – action A + 20 
 
if C views your decision. In both 
cases, the participant does not get the extra 20 points if C does not view his decision. 
B-13 
 
(4) The payof of C depends on the states, his own actions and the total cost of viewing the 
decisions of A and B participants. It is maximized by reporting the expected value of each 
state based on the information observed. 
 
Are there any questions?  
 
B-14 
 
 
 RECORD SHET 
 
 
 
 
Subject ID:      ______ 
 
 
 
 
TOTAL EARNINGS:     $___ 
 
 
 
 
 
 
Name:____________   Date:____________ 
 
  Amount received:_______ 
 
Schol ID #:_______________   Signature:___________ 
 
 
 
 
 
 
 
 
 
B-15 
 
[THE NEXT PAGE ONLY FOR THE EXPERIMENTER] 
 
[PAUSE to answer questions] 
 
------------------------------------------------------------------ 
 
We wil now begin the Practice sesion and go through 1 practice match to familiarize you 
with the computer interface and the procedures. During the practice match, please do not hit any 
keys until you are asked to, and when you enter information, please do exactly as asked. Remember, 
you are not paid for the practice match. At the end of the practice match you wil have to answer 
some review questions. Everyone must answer al the questions corectly before the experiment can 
begin. 
 
[AUTHENTICATE clients] 
 
Please double click on the icon on your desktop that says ____. When the computer 
prompts you for your name, type your First and Last name. Then click SUBMIT and wait for further 
instructions. 
 
[START game] 
 
You now se the first scren of the experiment on your computer. Raise your hand high if 
you do. Please do not hit any key. 
 
[PAUSE TO BE SURE EVERYONE HAS THE CORECT SCREN] 
 
At the top left of the scren you se your subject ID. Please record that on your record shet 
now. Some of you have Role A, some have Role B and some have Role C. If you have Role A or B, 
the scren loks similar to the screnshot in display 1. If you have Role C, you are instructed to wait. 
In al cases, at the botom of the scren you can se a history panel with al the information relevant 
for each match. 
 
 If you have Role A or B, and your subject ID is even, click on the “Transmit” buton. If it is 
od, click on the “Withold” buton. Note that it does not mater which one you chose since you wil 
not be paid for this match. 
 
If you have Role C, you should now se a scren similar to the screnshot in display 2. If you 
have Roles A or B, you are instructed to wait. Click on the butons to se A1’s decision then type the 
last two digits of your social security number and click “Submit”. 
 
If you have Role C, you should now se a scren similar to the screnshot in display 3. If you 
have Roles A or B, you are instructed to wait. Click on the butons to se B2 and B3’s decisions. 
Now, type the last two digits of your year of birth and click “Submit”. 
 
You should now al se a scren similar to the one in display 4. It displays the states, the 
actions of C and the payofs of al participants in your group. 
 
Now click “Continue”. The practice match is over. Please complete the review questions 
before we begin the paid sesion. Once you answer al the questions corectly, click submit. After al 
participants in your group have answered al questions corectly, the quiz wil disapear from your 
scren. Raise your hand if you have any question. 
B-16 
 
 
[WAIT FOR EVERYONE TO FINISH THE QUIZ] 
 
Are there any questions before we begin with the paid sesion? 
 
We wil now begin with the paid matches.  
 
Remember, in the next matches, for the participant in role C, the cost of viewing decisions of 
A and B participants are as folows. For the first decision of an A participant you view, the cost is 5 
points and for the second decision of an A participant you view, the cost is 30 points. For the first 
decision of a B participant you view, the cost is 10 points and for the second decision of a B 
participant you view, the cost is 50 points. 
 
[at the end of GAME __] 
 
The first part of the experiment is now finished. The second part of the experiment is 
identical to the first part except for the cost of viewing the decisions of A and B participants for the C 
participant. For the first decision of an A participant you view, the cost is now 10 points and for the 
second decision of an A participant you view, the cost is 50 points. For the first decision of a B 
participant you view, the cost is 5 points and for the second decision of a B participant you view, the 
cost is 30 points. 
 
[at the end of GAME __] 
 
This was the last match of the experiment. You wil be paid the payof you have acumulated 
in the __ paid matches. The payof apears on your scren. Please write this payof in your record 
shet and remember to CLICK OK after you are done. 
 
[CLICK ON WRITE OUTPUT] 
 
We wil now pay each of you in private in the next rom in the order of your Subject ID 
number. Remember you are under no obligation to reveal your earnings to the other participants. 
 
Please put the mouse behind the computer and do not use either the mouse or the keyboard. 
Please remain seated until we cal you to be paid. Do not converse with the other participants or use 
your cel phone. Thank you for your coperation. 
 
[CAL al the participants in sequence by their ID #] 
 
[Note to experimenter: use the “pay” file to cal and pay subjects] 
 
Could the person with ID number 1 go to the next rom to be paid? 
 
B-17 
 
FC – EXPERIMENT 2 (groups of 7) – INSTRUCTIONS – 01.17.201 
 
 Thank you for agreing to participate in this research experiment on group decision making. 
During the experiment we would like to have your undistracted atention.  Do not open other 
aplications on your computer, chat with other students, use your phone or headphones, read, etc.  
 
For your participation, you wil be paid in cash from a research grant, at the end of the 
experiment.  Diferent participants may earn diferent amounts.  What you earn depends partly on 
your decisions, partly on the decisions of others, and partly on chance. It is very important that you 
listen carefuly, and fuly understand the instructions. You wil be asked some review questions after 
the instructions, which you wil have to answer corectly before we can begin the experiment. 
 
If you have questions, don’t be shy about asking them. If you have a question, but you don’t 
ask it, you might make a mistake which could cost you money. 
  
The entire experiment wil take place through computer terminals. Al interaction betwen 
you and other participants wil take place through the computer interface. It is important that you not 
try to comunicate with other participants during the experiment, except acording to the rules 
described in the instructions. 
  
We wil start with a brief instruction period. During this instruction period, you wil be given 
a complete description of the experiment and wil be shown how to use the computers. At the end of 
the sesion, you wil be paid the sum of what you have earned in al matches. Everyone wil be paid 
in private and you are under no obligation to tel others how much you earned. Your earnings during 
the experiment are denominated in points. At the end of the experiment you wil be paid $1.0 for 
every _160_ points you have earned. 
 
 At the begining of the experiment, you wil be grouped with six other participants. Since 
there are __ subjects in today’s sesion, there wil be __ groups of seven. You are not told the 
identity of the participants you are grouped with. Your payof depends only on your decision and the 
decisions of the participants you are grouped with. What hapens in the other groups has no efect on 
your payof and vice versa. Your decisions are not revealed to participants in the other groups. 
 
 In each group, there wil be thre types of roles, Role A, Role B and Role C. There wil be 
thre participants in Role A, caled A1, A2, A3 participants, thre participants in Role B, caled B1, 
B2, B3 participants and one participant in Role C, caled C participant. You wil have either role A, 
role B or role C. Which role you have is randomly selected at the begining of the experiment and is 
clearly displayed on the scren. You wil kep the same role and wil be in the same group with the 
same participants for the entire duration of the experiment. 
 
The experiment wil consist of several matches. In each match, the computer wil draw two 
numbers. Each of these numbers can be any number betwen 0 and 10 and al numbers are equaly 
likely. These numbers are caled state A and state B. 
 
What to do 
 
If your role is A1, A2 or A3 (you are an A participant) the computer wil disclose state A to 
you but not state B. Similarly, if your role is B1, B2 or B3 (you are a B participant) the computer wil 
disclose state B to you but not state A. Al A participants se the same state A, and al B participants 
se the same state B. You wil then have to chose whether to “Transmit” or “Withold” the state. 
B-18 
 
You wil not se the decision selected by any of the other A or B participants when you make your 
decision. You wil then be instructed to wait. 
 
If you are a C participant, you wil be instructed to wait until al A and B participants have 
each chosen an action (“Transmit” or “Withold”). Then, you wil see six butons that hide the 
decision of each A and B participant. 
 
You wil first have the posibility to view the decision of each A participant. If you click on 
one of the A butons (A1, A2 or A3), the computer wil reveal state A if that A participant chose 
“Transmit” and state “unknown” if that A participant chose “Withold”. You can then view the 
decision of another A participant, and so on. Notice that if two or more A participants decided to 
“Transmit” and you view their decisions, the same number is revealed to you, namely state A. It is 
entirely your decision to view none, one or more decisions of the A participants. If you chose to 
view the decision of one A participant, it is also your choice whether to view the decision of A1, A2 
or A3. Finaly, there are costs of viewing these decisions. When you decide to not view any more 
decisions of A participants, you must take action A, which consists in typing a number betwen 0 and 
10. You then ned to click “Submit”. 
 
You wil then repeat the same steps regarding B participants. The only diference is that the 
costs of viewing the decisions of the B participants are diferent, as explained after. When you decide 
to not view any more decisions of B participants, you must take action B, which consists in typing a 
number betwen 0 and 10. You then ned to click “Submit”. 
 
When the C participant has made his decisions, the computer reveals the states A and B and 
displays the actions A and B selected by the C participant. Each participant can also se the payofs of 
al the participants in the group. 
 
When al groups have finished the match and have sen the results, we proced to the next 
match. For the next match, the computer randomly selects two new numbers betwen 0 and 10 
which corespond to the new states A and B. In the new match, you wil be in the same group with the 
same participants and you wil kep the same Role. Also, at the botom of the scren you wil se a 
History sumarizing what has hapened in the past matches of your group: which A and B 
participants chose to transmit and which ones chose to withold, which decisions of As and Bs the C 
participant chose to view, what were the states A and B and what were the actions A and B taken by 
the C participant. 
 
How much you get 
 
If you are an A participant, your payof is 50 plus the diference betwen action A and action 
B. Furthermore, if C viewed your decision, then you also get an extra 20 points. Therefore, you want 
C (i) to view your decision (for 20 points), (i) to chose an action A as high as posible, and (ii) to 
chose an action B as low as posible. 
 
If you are a B participant, your payof is 50 plus the diference betwen action B and action 
A. Furthermore, if C viewed your decision, then you also get an extra 20 points. Therefore, you want 
C (i) to view your decision (for 20 points), (i) to chose an action B as high as posible, and (ii) to 
chose an action A as low as posible. 
 
If you are a C participant, your payof depends on both states and on both actions, and it is 
decreased by the total cost of viewing decisions of A and B participants. It is equal to: 
 
B-19 
 
120 – (state A – action A)
2
 / 40 – ( state B – action B)
2
 / 40 – cost of viewing As and Bs 
decisions. 
 
Note that you maximize your earnings if you chose each action equal to the expected value 
of the coresponding state. To se this, supose for simplicity there is only state A, and supose there 
is 50% chance that state A is 20 and 50 % chance it is 40, the amount you earn in expectation is: 
 
120 – 0.5(20- action A)
2
 / 40 – 0.5(40- action A)
2 
 / 40 –cost of viewing As and Bs decisions 
 
Therefore if you chose action 20 or 40, your payof is 15 – cost of viewing As and Bs decisions. 
Instead, if you chose 30 (that is, 20*0.5 + 40*0.5), your payof is 17.5 – cost of viewing As and Bs 
decisions. Naturaly, if you know one of the states for sure, then you should chose the action for that 
state equal to the state. 
 
The cost of viewing the decisions of A and B participants are as folows. In the first part of the 
experiment, the first decision of an A participant you view costs _5_ points (it is the same cost for 
viewing the decisions of A1, A2 or A3). The second decision of an A participant you view costs 
_30_ points. You canot view the decision of al thre A participants. Similarly, the first decision 
of a B participant you view costs _10_ points, and the second decision of a B participant you view 
costs _50_ points. You canot view the decision of al thre B participants. The costs in the 
second part of the experiment wil be reversed, and wil be clearly explained when we reach that 
stage.  
 
There wil be one practice match. The points acumulated in this match do not count towards 
your final dolar earnings. The practice match is similar to the matches in the experiment. 
 
Before the practice match, we wil present the game using screnshots. It is important that 
you understand this information. If you have a question during this presentation, raise your hand and 
we wil answer you. 
 
Display 1. Sample screnshot for A and B participants 
This scren is displayed to you if you are either an A or a B participant. The exact Role is displayed at 
the top of the scren. In that example, you are participant B1. 
 
B-20 
 
  
In that match, state B is 19. You have to chose betwen “Transmit” or “Withold” the state. You 
simply ned to click the coresponding buton. 
 
Display 2. First sample screnshot for C participant 
This scren is displayed to you if you have Role C and after al A and B participants have made their 
decisions. 
 
You have the posibility to view the decisions of A1, A2 and A3. You must then enter a number in 
the box and click “Submit”. Notice that below those boxes are butons to view the decisions of B 
participants, but they are disabled at this point. 
 
Display 3. Second sample screnshot for C participant 
 
This scren is the second scren you se when you have Role C. Once you have submited your 
decision regarding state A, the butons to view the decisions of A participants are disabled. The 
number you submited is also visible but you canot change it anymore.  
 
B-21 
 
In this example, you viewed the decision of A1 who transmited the state, so you learned that 
state A was 61. You also viewed the decision of A2 who chose to withold the information. Finaly, 
you chose action 9. Note that this is an ilustration: the decisions and numbers only reflect a 
randomly generated behavior. 
 
Now, you have the posibility to view the decisions of B1, B2 and B3. Last, you must enter a 
number in the box and click “Submit”. 
 
Display 4. Sample screnshot of the last scren 
 
This is the last scren you se in the match. Al participants se the exact same scren, except for the 
top line that displays only your role. 
 
 
The scren shows the states A and B, the actions A and B chosen by the C participant and the payofs 
of al participants in the group. To reach the next match, you ned to click “Continue”. 
 
Notice that at the botom of the scren, you can also se the history of previous matches. For each 
match, the scren shows the states A and B, the decision of each A and B participant, whether C 
viewed the decisions of each of the A and B participants, and the actions A and B chosen by C. This 
history scren is important as it tracks the past behavior of each participant. 
 
Recap 
 
 Here is a brief recap of the important things you wil se, and how they afect your payofs: 
 
(1) Roles A know state A and can chose to “Transmit” or “Withold” it to C. Similarly, Roles B 
know state B and can chose to “Transmit” or “Withold” it to C. 
(2) If C clicks on a participant’s buton, C wil learn the state if that participant chose “Transmit” 
and he wil se “unknown” if that participant chose “Withold”. Clicking on a participant’s 
buton is costly. 
B-22 
 
(3) The payof of an A participant is 50 + action A – action B + 20 
 
if C views your decision. The 
payof of a B participant is 50 + action B – action A + 20 
 
if C views your decision. In both 
cases, the participant does not get the extra 20 points if C does not view his decision. 
(4) The payof of C depends on the states, his own actions and the total cost of viewing the 
decisions of A and B participants. It is maximized by reporting the expected value of each 
state based on the information observed. 
 
Are there any questions?  
 
B-23 
 
 
 RECORD SHET 
 
 
 
 
Subject ID:      ______ 
 
 
 
 
TOTAL EARNINGS:     $___ 
 
 
 
 
 
 
Name:____________   Date:____________ 
 
  Amount received:_______ 
 
Schol ID #:__________   Signature:___________ 
 
 
 
 
 
 
 
 
 
B-24 
 
[THE NEXT PAGE ONLY FOR THE EXPERIMENTER] 
 
[PAUSE to answer questions] 
 
------------------------------------------------------------------ 
 
We wil now begin the Practice sesion and go through 1 practice match to familiarize you 
with the computer interface and the procedures. During the practice match, please do not hit any 
keys until you are asked to, and when you enter information, please do exactly as asked. Remember, 
you are not paid for the practice match. At the end of the practice match you wil have to answer 
some review questions. Everyone must answer al the questions corectly before the experiment can 
begin. 
 
[AUTHENTICATE clients] 
 
Please double click on the icon on your desktop that says ____. When the computer 
prompts you for your name, type your First and Last name. Then click SUBMIT and wait for further 
instructions. 
 
[START game] 
 
You now se the first scren of the experiment on your computer. Raise your hand high if 
you do. Please do not hit any key. 
 
[PAUSE TO BE SURE EVERYONE HAS THE CORECT SCREN] 
 
At the top left of the scren you se your subject ID. Please record that on your record shet 
now. Some of you have Role A, some have Role B and some have Role C. If you have Role A or B, 
the scren loks similar to the screnshot in display 1. If you have Role C, you are instructed to wait. 
In al cases, at the botom of the scren you can se a history panel with al the information relevant 
for each match. 
 
 If you have Role A or B, and your subject ID is even, click on the “Transmit” buton. If it is 
od, click on the “Withold” buton. Note that it does not mater which one you chose since you wil 
not be paid for this match. 
 
If you have Role C, you should now se a scren similar to the screnshot in display 2. If you 
have Roles A or B, you are instructed to wait. Click on the butons to se A1’s decision then type the 
last two digits of your social security number and click “Submit”. 
 
If you have Role C, you should now se a scren similar to the screnshot in display 3. If you 
have Roles A or B, you are instructed to wait. Click on the butons to se B2 and B3’s decisions. 
Notice that once you have sen the decisions of two B participants you canot click on the 
decision of the third. Now, type the last two digits of your year of birth and click “Submit”. 
 
You should now al se a scren similar to the one in display 4. It displays the states, the 
actions of C and the payofs of al participants in your group. 
 
Now click “Continue”. The practice match is over. Please complete the review questions 
before we begin the paid sesion. Once you answer al the questions corectly, click submit. After al 
B-25 
 
participants in your group have answered al questions corectly, the quiz wil disapear from your 
scren. Raise your hand if you have any question. 
 
[WAIT FOR EVERYONE TO FINISH THE QUIZ] 
 
Are there any questions before we begin with the paid sesion? 
 
We wil now begin with the paid matches.  
 
Remember, in the next matches, for the participant in role C, the cost of viewing decisions of 
A and B participants are as folows. For the first decision of an A participant you view, the cost is 5 
points and for the second decision of an A participant you view, the cost is 30 points. For the first 
decision of a B participant you view, the cost is 10 points and for the second decision of a B 
participant you view, the cost is 50 points. You canot view the decision of al thre A 
participants or al thre B participants. 
 
[at the end of GAME __] 
 
The first part of the experiment is now finished. The second part of the experiment is 
identical to the first part except for the cost of viewing the decisions of A and B participants for the C 
participant. For the first decision of an A participant you view, the cost is now 10 points and for the 
second decision of an A participant you view, the cost is 50 points. For the first decision of a B 
participant you view, the cost is 5 points and for the second decision of a B participant you view, the 
cost is 30 points. You canot view the decision of al thre A participants or al thre B 
participants. 
 
[at the end of GAME __] 
 
This was the last match of the experiment. You wil be paid the payof you have acumulated 
in the __ paid matches. The payof apears on your scren. Please write this payof in your record 
shet and remember to CLICK OK after you are done. 
 
[CLICK ON WRITE OUTPUT] 
 
We wil now pay each of you in private in the next rom in the order of your Subject ID 
number. Remember you are under no obligation to reveal your earnings to the other participants. 
 
Please put the mouse behind the computer and do not use either the mouse or the keyboard. 
Please remain seated until we cal you to be paid. Do not converse with the other participants or use 
your cel phone. Thank you for your coperation. 
 
[CAL al the participants in sequence by their ID #] 
 
[Note to experimenter: use the “pay” file to cal and pay subjects] 
 
Could the person with ID number 1 go to the next rom to be paid?