FCC Media Study No. 9:
A Theoretical Analysis of the Impact of Local Market Structure
on the Range of Viewpoints Supplied
Isabelle Brocas, Juan D. Carrillo, Simon Wilkie
Department of Economics University of Southern California
1
Table of Contents
1. Executive Summary..............................................3
2. Institutional Background......................................5
3. Literature Review.................................................7
4. Blackwells Theorem and Media Markets.............12
5. Model Preliminaries............................................18
6. Competition Model 1..........................................19
7. Competition Model 2..........................................23
8. Competition Model 3......................................... 27
9. Experimental Design ........................................ 29
10. Experiment 1 Results.......................................33
11. Experiment 2 Results.......................................39
12. Conclusions.......................................................47
2
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 Blackwells comparison of experiments, to measure the quality and
diversity of information transmitted in the market and how that quality in turn af-
fects welfare. We argue that Blackwells method is the appropriate theoretical metric
to measure the market place for ideas.
We consider the case of where a decision maker (e.g., a voter) requires infor-
mation 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 or opinion that will be 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 consider that expertise the expression of the 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 ex-
hibit some bias and garbling. This causes a welfare loss to information consumers.
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 equilib-
rium 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
bias diminishes and consumer welfare increases. We model these costs as reputation
costs. That is if two media outlets have similar viewpoints then one with the greater
reputation for being informative will have the greater audience 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 diversity of
ownership is required not just to obtain diversity of viewpoints, but in addition it
3
is competition among firms with the same viewpoint drives informational efficiency.
Thus, informational concerns for diversity and localism may require ownership limits
more stringent than would be justified by conventional anti-trust analysis alone.
We then test the model with experimental treatments. The treatments that
consider the roles of; biasing, garbling, and reputation cost. We find that our
theoretical models do quite well at predicting behavior. In general, media firms do
behave strategically and 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 t of a particular class
of broadcast license (TV or radio)wo, 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 FCCs
diversity and localism goals.
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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 be 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 necessary includes three elements. They are; 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 had as developed several specific rules
that limit are 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 Com-
munications 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, un-
der 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 pub-
lic 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
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 Re-
consideration, available at http://hraunfoss.fcc.gov/edocs public/attachmatch/FCC-07-216A1.pdf
and 2002 Biennial Regulatory Review: Report and Order and Notice of Proposed Rulemaking;
See 2002 Biennial Regulatory Review Review of the Commission’s Broadcast Ownership Rules
and Other Rules Adopted Pursuant to Section 202 of the Telecommunications Act of 1996, Report
and Order and Notice of Proposed Rulemaking, MB Docket No. 02-277, MM Docket Nos. 01-235,
5
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
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 Commissions
diversity and localism goals, thereby supplementing the empirical analysis in other
studies.
The approach assumed in this paper is that the Commissions 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 and 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 converntial media sources on the web such as: NBC.com,
01-317, 00-244, 03-130, 18 FCC Rcd 13620 (2003), aff’d in part and remanded in part, Prometheus,
373 F.3d at 435, stay modified on rehearing, No. 03-3388 (3d Cir. Sept. 3, 2004) (Prometheus
Rehearing Order), cert. denied, 545 U.S. 1123 (2005)
6
New York Times.com Washington Post.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 ones location such that the rules on ownership at the national level
largely irrelevant. When we turn to coverage of the local market however there
seems to be much more relevant concentration and in particular the lack of diversity
of authoritative and reliable news sources at the local level comparede with those
that that exist at the national level. Therefore, our focus in this study is at the local
level where there may be just a few broadcast television and radio stations, and an
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, much of the
most important and relevant literature is very recent and area of media economics
is developing rapidly.
Early work studying the media goes back to of course 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 programming mix or radio format. In Steiner’s radio model one obtains the
following result. If we have a a mass of consumers located centrally along a line
which we might think of as the diversity of viewpoints from left to right or from
lowbrow to highbrow television, and the distribution is single peaked, then the
largest mass audience would 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 firm 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 for the audience
to the right so the equilibrium is that firms choose the same spatial location and
split the market 50-50. However, entry is bad for the first firm as the entrant is now
cannibalizing the market of the existing firm. Therefore, if instead we introduce the
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second license and allocated it to the incumbent, the monopolist oner of two licenses
(or duopolist in FCC parlance) would in fact choose to relocate both firms and spread
them out so that they didn’t cannibalize each other’s market. Therefore, the Steiner
result is that we would have greater diversity with monopoly then we would under
competition. In an empirical paper Berry and Waldfogel 2001 test this result by
examining the impact of radio mergers on a stations format choice. They indeed
find support for the result. However, although interesting is naturally somewhat
limited application to format choice rather than viewpoint. In particular, firms
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 profit driven or preference reasons.
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. Moreover, the
Steiner result is not robust the introduction of the third firm or even higher numbers
of firms it becomes very difficult to describe what will be equilibrium allocation of
firms.
Influential work on the regulation of television is done by in the 1970s and 80s
by economists in the so-called ”public choice” framework. In particular the work
”Misregulating Television: network dominance and the FCC, by Stanley Besson
et. al. (1984) investigated the role of the FCC in terms of limiting entry into the
market and also a enforcing vertical contracting relations between networks and
their affiliate stations and they investigated he issue of 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 house analysis most of this literature is empirical and it begins with classic
paper by Jeff Dubin and Matt Spitzer (1993) investigated if the ownership structure
affected the choice of format in radio. In that study they found that the race of the
owner affected the probability that 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
of the paper by Siegelman and Waldfogel (2001) replicated these results. That study
found that in particular the ownership structure not only affects the format but also
probably affects the welfare market that minority audiences increase with minority
ownership. Obelholzer-Gee and Waldfogel (2006) found that has implications for
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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 voter use information and affects their behavior see the book Information
and Elections by R. Michael Alvarez (1998). In particular, Alvarez examines several
presidential elections and finds that if a voter has 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 a
voter has also affect 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
the quality of information. 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
Ghiradato (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
FCCs localism concerns. In this study we show that the quality and diversity of
information in turn is linked to market structure.
There, is long literature examining media bias and many popular works on the
topic that we will not review here as most of it is beyond our expertise. Recently,
there has been a new and sophisticated analysis of measures of media bias or slant
using econometric techniques. At the outset it should be said when this literature
uses the word bias, the word here as equivalent viewpoint at this point in time, we
will define the difference in the model below. In particular the recent work by Tim
Groseclose and Milyo (2005) provides a careful study of the viewpoint or bias of
different media. They find that indeed there is a difference of viewpoint and that
different media institutions are well associated with a particular left of centre or
right of centre view. For instance the New York Times is recognized as being a
left of centre viewpoint, and the Fox News Channel is recognized as being a rate of
centre viewpoint. There are less centrist newspapers.. These findings have also been
found in other studies using similar methodologies including Gentzkow and Shapiro
9
(2010).
Following up this work a recent paper by Delavigna and Kaplan (2006) that stud-
ies 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 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 others in what appears to be a some-
what random fashion because of the quilt of ownership of cable networks platforms
in the United States. Given this randomized ”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 Delavigna and Kaplan find
is that indeed there is an impact of the Fox News introduction, and that that results
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 exposure to the information transmitted
by Fox News changed opinions. In a related study experimental study, Gerber Kar-
lan and Bergan (2009), randomly assigned households free subscriptions to either
the Washington Post or the Washington Times. They find that those assigned to
the Washington Post treatment group, were eight percentage 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 informational content of a media
market can have an effect on how people make decisions such as choosing whether
or not to vote and indeed the choices that they make. Therefore, 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.
In addition, there are several recent theoretical papers examining media compe-
tition and information transmission, that are closely 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. We begin with the paper the ”Market for News” by
Sendhil Mullainathan and Andrei Shleifer (2005) which is typical of these papers.
This paper builds on the behavioral economics work of Matt Rabin and Joel Schrag
10
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 information that confirms the
prior belief or bias. This type of model of consumer behavior is adopted in their
study, and they examined the impact of competition when consumers are distributed
with certain biases such as people prefer left-wing information or people are right
wing. They find that the market will be characterized by polarization and firms
offering different viewpoints opinion both of these media sources will in equilibrium
be biased. Although this model is extremely interesting it has two limitations for
the point of view of the FCC’s exercise in examining the role of the media owner-
ship 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 should the FCC except consider these biases at all, or are these biases is actu-
ally a good thing or a bad thing to consider 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 being offered
here is increasing polarization in society and leading to people making 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. That is when consumers
do not receive the correct signal agents do not make inference that should be made
given the media bias. The fully rational agents in the model developed below we
incorporate exactly these features. Therefore, although this model 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 are unable to make any definitive
judgments as to whether or not this is in the public interest. Moroever, we are
also unconvinced that behavioral biases are the sole factors driving viewpoint diver-
sity. 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 viewers prior belief
rather than a behavioral bias per-se. Like the model in this study Gentzkow and
Shapiros consumers are rational in that correctly update their belief upon seeing an
uninformative signal.
The closest papers to the current study is the paper by Anderson and McLaren
11
(2010). In particular they includes a ”supply side bias” model where the media
owners may choose to transmit information or bias the signal by withholding infor-
mation to the citizen 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. Their papers characterize the equilibrium with a single owner
of the media outlets and compare that with the introduction of a second owner.
They find that the amount of information transmitted increases and that there is
a positive impact on diversity of viewpoint through the impact of competition. In
particular, their model is closely related to our Model 1 below, however they also
include price competition and our model 1 can be seen a s a special case of their
model. Unsurprisingly our results and conclusions are very similar. Finally although
there is costly communication in our model, we also mention that there is a link
between our work and the models of “cheap talk” with multiple senders, for example
Krishna and Morgan (2001).
4 Blackwells Theorem and Measuring Welfare in
Media Markets
The approach adopted in this study is that the media markets functions as an
information market, it provides signals to a citizen, or information consumer, who
uses the signal to choose a belief or 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 the consumers utility creases then she is better off. This simple
observation is that if a change in ownership structure leads to better information
and as a result the consumers are better off, then this in the public interest.
Our analysis begins primarily with the beautiful theorem of David Blackwell
(1953). 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
was that the two different measures turn out to be mathematically equivalent. The
first measure is purely statistical, based on information theory and signal transmis-
sion and the second measure based on the economic intuitive economic notion that
better information is more valuable to the decision maker because 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
12
if the first information structure is better than information structure be under the
second or economic criteria. This implies that if we can show one media market
ownership structure results in a more informative market in teh statistical sense,
then it leads to higher consumer welfare, even if we do not know the consumer’s
utility function! The approach adopted in our study is to adapt Blackwell’s com-
parison 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 in the mar-
ket and the structure of the ownership in the market, firms go 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 i.e. view the channel or
listen to the radio broadcast, and once receiving the signal 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 making and action. The informed citizens use this information they
make the action to maximize 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 that is 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 would compare to the market structures and
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 (1951). That is, the primary concept
here is that there is a set of states of the world which we will denoted S, and a
set of actions, A that can be chosen by a decision maker, Given that the state of
the world is s
i
and the decision-maker chooses action a, the decision maker receives
a utility of that choice which is denoted U(a, s
i
). The decision maker has a prior
probability distribution over the state’s p(s) where for all s
i
? S, p(s
i
) ? 0 and
summationtext
s?S
p(s
i
) = 1. Given any choice that induces a random utility outcome over the
states. The consumer chooses an action to maximize the following expected utility
13
functional
summationtext
s?S
p(s)U(s
i
, a). In this section will assume that the state space is finite
as is the signal space, however this is to aid the exposition. In the following sections
we will use convex compact state spaces and continuous probability measure rather
than sums, but the concepts are the same.
There is a set of possible signal outcomes denoted T = (t
1
, t
2
, . . . , t
k
).
An experiment or signal or in our context media information transmission, is
a random variable or a n × k Markov Matrix [X] where x
ij
is the probability of
observing signal j when the true state of the world is Media outlet i, that for all i, j
x
ij
? 0 and for all states i ? S,
summationtext
k
j=1
x
ij
= 1.
Given a signal [X] a decision maker will upon observing the signal outcome
t
j
update her belief about the probabilities of the true state q(s|t
j
), (i.e., 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
j
)U(a, s
i
).
Let the path of action a
?
(X, t
j
) be the solution the maximization problem, that
is the optimal action given information structure [X] after observing signal t
j
.
Define the value of experiment or information structure [X] as:
V (X) =
summationdisplay
ij
x
ij
U(a
?
(X, t
j
)s
i
).
We will say that X
1
is more informative that X
2
or X
1
followsequal X
2
if V (X
1
) ? V (X
2
),
if the decision maker has at least as high an expected utility upon acting on the
signal X
1
as acting 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
equal to X
1
plus some noise.
We can now state the theorem:
Proposition 1 The experiment [X
1
] is more informative than [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 1, High is optimal action and in state 2, Low is the
optimal action. Assume that the utility of choosing the correct action is 1 and the
wrong action is 0. Suppose that signals can have three values ”High” ”Medium”
14
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
1
X
2
X
3
S
1
0.5 0.5 0.00
S
2
0.00 0.5 0.5
TABLE A.4b: Signal [Y]
Y
1
Y
2
Y
3
S
1
1/3 1/3 1/3
S
2
1/3 1/3 1/3
In this case [X] is preferred to [Y ]. To see this consider observing the signal X
1
.
The agent knows that the true state is S
1
and so the agent chooses ”High.” Similarly
if the agent observes X
3
she knows the state is S
2
and she choose Low. Observing
X
2
she knows each outcome is equally likely and so randomizes if she is indifferent.
Notice that agent picks the optimal action 75% of the time. Now consider and signal
Y
j
, as it is equally likely that that signal was generated in either state the signal
provides 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, or
”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 off states after
we eliminate redundant signals, such that 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
where we learn nothing from the signal and the decision maker continues to hold her
prior belief after every signal, the matrix where every element is 1/n. That signal we
will label [J] for jamming signal although we could also label it a Spamming Matrix
as it spans the null space. It will be shown that in the next section the media outlets
will either use [I] or degenerate uninformative signal as conditional signals.
15
TABLE A.4c: Signal [I] ”Full Information”
I
1
I
2
I
3
S
1
1.0 0.0 0.0
S
2
0.00 0.0 1.0
TABLE A.4d: Spamming Matrix [J]
1/3 1/3 1/3
1/3 1/3 1/3
1/3 1/3 1/3
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 do no need to know to make
welfare comparisons. In particular Blackwell’s Theorem does not require us to know
the utility function or the decision makers prior preference or beliefs. In 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 that ”a market with four independent firms is better than two” and
” in experiments the market with six firms performed better than the market with
four firms.”
4.1 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 work of Paul Milgrom in his paper Good News
and Bad News: Representation Theorems and Applications (1981). In Milgrom’s
model there one agent, a sender who we think of as a salesman, who has observed
the value of a random variable x
prime
? X and choose to make a report to a second
agent (a buyer) who 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
16
buyer towards a purchase. We assume that he can report any S ? X with x
prime
? S.
Thus, the salesman cannot deliberately lie but can very uninformative by reporting
a large S. Notice in particular that if S ? T then S is more informative than
T in Blackwell’s sense. Milgrom’s remarkable result is that the salesman should
report the simple truth, x
prime
. The logic is known as ”unravelling.” That is, if they
buyer sees some set S he knows the true value is in S 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 S 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 S either
and so on.... Thus the only consistent beliefs are, that on seeing a set S the truth
is the worst point in S. That is, ”no news is bad news.” Therefore, the salesman
cannot gain by withholding information. In our context this 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 unravelling result depends on certain key assumptions: In
particular the buyer/decision maker knows the bias of the sender, and the infor-
mation structure is common knowledge. Second the sender always knows the true
value of x. If there is some small probability that sender does not know the true
value then we shall show that complete unravelling fails. Finally there is the ”grain
of truth” assumption that the sender cannot deliberately mislead the receiver by
giving false information- only fuzzy information 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 uniformative signal is observed it could be that the sender is uniformed.
In our second model will allow for limited “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 limited unravel-
ling still occurs and the media will either be fully informative or uninformative. In
particular we assume that if the media outlet receives no signal it can only report
17
a known ”no news” signal which would be equivalent to reporting the full set X in
Milgrom’s model. Thus, if a media outlet tries to hide bad news (from its perspec-
tive) it will send the uninformative signal, as any other signal such as a set S will
be recognized as not sent by an uniformed party and unravelling will hold on that
set S. 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 increases welfare.
5 Model Preliminaries
Consider two media outlets, or editors, that support opposite political policies or
parties, A and B ( the media will be indexed by i and j with i negationslash= j). With opposite
editorial or political views the media may be competing to influence citizen decision
makers who may be thought of as information consumers or voters. From now on, we
will use the canonical case of competing to influence voters. In particular we adopt
the model used in Political Science known as electoral competition with “valence.”
That is there is a one dimensional policy space ranging from ”Low” to ”High” 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. A High level of expenditure
means higher taxes and low level means lower taxes. Some voters will prefer a higher
level of expenditure (and therefore taxes) while other voters will prefer a lower level
of expenditure. The are two options, one of which must be chosen which we think of
political parties. We know that each Media outlet i will implement a given policy.
However, following Stokes (1963) the decision maker also cares about the quality
or competence of the elected official, this property is known as valence, see also
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 the policy is far from
her ideal point, over an incompetent -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 competition for the median voter that determines the outcome.
Formally:
• Quality. The quality of Media outlet i observes the valence or quality of
18
candidate i ?
i
? [?,?]. We assume that ?
i
is drawn from a distribution with c.d.f.
F
i
(?
i
).
• Location.The policy space is the unit interval [0, 1]. Parties are located at the
two extremes of the Hotelling line. Media outlet i A is located at z = 0 and Media
outlet i B is 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 electing a Media outlet i is equal to
the Media outlet i’s quality minus the Euclidian distance between the voter’s ideal
position and the position of the Media outlet i. Formally, u
z
(A) = ?
A
?z if Media
outlet i A is elected and u
z
(B) = ?
B
?(1?z) if Media outlet i B is elected. Given
such preferences a voter strictly prefers to elect Media outlet i A if he is located at
z < z
?
and Media outlet i 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, it is formally identical to consider
a continuum of voters with z representing the location of the median voter).
• Media owners’ preferences. Parties only care about winning the election. The
media owner is interested in the probability that her preferred candidate (or view-
point) wins Denote by
˜
?
i
Media outlet 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 the Media outlet i). This inferred quality is what the voter uses for his decision.
The utility of Media outlet i, ?
i
, is simply the probability of winning the election
given the inferred qualities of both parties:
?
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” that is they would prefer to see a particular Media outlet i win the election.
19
However the media outlet may not know their parties own quality. Because we
associate each media outlet with preference for a Media outlet i, we will just use
the shorthand ”Media outlet i” in the analysis below. More precisely, consider the
following setting.
• Information. Media outlet Media outlet i observes signal ?
i
= ?
i
with proba-
bility 1?p
i
and observes nothing ?
i
= ?
i
with probability p
i
.
• Disclosure. We take a very simple approach to disclosure. We assume that
parties can withhold information but cannot report false or inaccurate information.
More precisely, the report r
i
(?
i
) of Media outlet 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 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 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 Media outlet 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 Media outlet i’s utility is increasing in
˜
?
i
and decreasing
in
˜
?
j
, that is, a Media outlet benefits when his perceived quality is high and the
perceived quality of the rival is low. In fact, given ?
i
, the objective function of
Media outlet 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
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 Media outlet i reports ?
i
, the voter’s belief
˜
?
i
cannot
depend on the realized quality. Conversely, when Media outlet 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 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]
20
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
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 cutoff x
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 of not receiving information, x
i
(p
i
), are summarized
below.
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)
21
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
].
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 and Roberts (1986) holds: the highest quality Media outlet i always
has an interest in revealing his type, then so does the second highest quality Media
outlet i, 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,
low quality informed parties may pool with uninformed parties and choose not to
disclose their information. In that case, no information revelation can occur in
equilibrium even in the absence of a disclosure cost. As parties become more likely
to be (exogenously) uninformed, the incentives of informed parties to pool are higher,
so the cutoff x
i
increases. When parties almost never obtain information (p
i
? 1)
voters infer the expected quality so any informed Media outlet i with quality below
E
i
[?
i
] would choose not to disclose his type. Finally, notice that the utility of parties,
?
i
, is additively separable in the inferred qualities of both parties, (
˜
?
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
show that welfare increases with two media outlet owners versus a single monopolist
22
owner who will supply only one viewpoint. A similar result obtains in our model.
We finally illustrate the result with a simple 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 parties
always observe qualities (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 his quality ?
i
. The
new option is that, in case of disclosure, Media outlet i j can now choose whether
to allow (r
j
i
(?
i
) = ?
i
) or garble (r
j
i
(?
i
) = ?
i
) the information regarding Media outlet
i. If Media outlet i discloses and Media outlet i j allows information, then the voter
learns ?
i
. Conversely, if Media outlet i withholds or Media outlet i discloses but
Media outlet i j garbles the information, then the voter obtains no information.
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 i. 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.
3
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
information whereas Media outlet i 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
i needs to spend resources to try and “mislead” the voter by either withholding
evidence about himself or suppressing evidence about the opponent. However, our
3
For example there are many websites with respectively left wing or right wing viewpoints that
claim to document instances of mis-represntation by the media outlets.
23
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 i’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 station and so the firms audience
share and profits will fall.
• Timing. The new timing of the game is the following. First, each Media outlet
i and j decides whether to disclose or withhold information. Second, if information
is withheld, Media outlet i j and Media outlet j 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. In either case, she
decides which party 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 i to act on
Media outlet j’s information will never depend on the quality of j. 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 outlet i and j have cutoff strategies regarding the decision to with-
hold and suppress information on Media outlet i’s quality, respectively. 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
))
24
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 i 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 parties Media
outlet 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.
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
)
that is if ?
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
that is if ?
B
< y ? E
B
(?)?d. Note that E
B
(?) = E[?
B
|?
B
? [?
B
, y[
uniontext
[y,?
B
]] and we
have the following equality:
y + d = E[?
B
|?
B
? [?
B
, y[
uniondisplay
[y + d + c,?
B
]]
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
25
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 to d (respectively c), 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 withhold
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 information and
Media outlet j to garble the best possible one. An unraveling argument applies
simultaneously to both sides, which results in a complete suppression of informa-
tion by one of the parties. 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 i 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 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 has less incentives to do so. Formally,
26
y
i
increases. We now 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” firm and which firm is being informative.
Suppose now that the market structure was just two firms one representing each
viewpoint and the consumer an uninformative signal. With just two firms one with
each viewpoint, the consumer is unable to distinguish which firm to punish and
which firm to ”trust.” Moreover, the consumer has no choice but to tune into both
sources to collect information.
However, now suppose that there are four firms, with two firms of each viewpoint.
Suppose that media outlets 1 and 2 favor party A and firms 3 and 4 favor party
B. In addition suppose that the consumer faces a (perhaps very small) cost, epsilon1 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 second sourcing with firm 2 because whenever firm’s 1
27
signal is uninformative, so is firm 2’s. Therefore we conclude that (i) the strategy
of firm 2 cannot influence the decision maker, and (ii) firm 2 receives no audi ence
share (i.e., it incurs the cost). 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 change its
strategy so it that 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:
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 In-
formational Bertrand Competition the equilibrium becomes fully revealing, 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 witholding - 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 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 informa-
tion form 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 cap-
tures all the market and so increases its profits discretely by M/2. Thus again there
will be an unravelling 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
28
Informational Bertrand Competition is obviously an extreme assumption, but
it obtains a strong result full information efficiency with 4 firms when there are
two firms of each viewpoint. like the standard Bertrand model we think of this as
being a benchmark that provides useful insight. In particular it may be that there
is still a 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 their
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 5th firm could add viewpoint diversity and a sixth firm with
that underrepresented viewpoint will induce competition and so there will be a
probabilistic increase in welfare. To address these concerns we adopted experimental
techniques as reported in the next section.
9 Experimental design and procedures
We tested in the laboratory Models II and III, from now on labeled experiments
1 and 2. Although Model 1 provides the basic framework for our analysis we did
not test Model I 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, although it provides an interesting reason for non-
disclosure (veil of ignorance) but, in our view, it is 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.’
4
No subject participated in more than one session. For
each session in experiment 1, twelve subjects were randomly assigned in groups of
4
Documentation and instructions for downloading the software can be found at
http://multistage.ssel.caltech.edu.
29
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 at the session and remained in the same group until the end of
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.
5
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. They had to decide independently and simulta-
neously whether to disclose the state to agent C. If A (respectively B) decided to
withhold 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 to with-
hold, then C would observe “state is unknown” but not the identity of the player
responsible for withholding. The 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
5
Sample copies of the instructions are attached in the Appendix.
30
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.
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.
31
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 payer 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 the 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 was costly to C but yielded a benefit to the 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 Media outlet i, z
i
is the action taken by C regarding state Media
outlet 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 decision in order to obtain the extra payoff. This captures reputation
effects. Also and as in experiment 1, the quadratic scoring rule implied that subjects
32
in role C should take the action closest to their expected belief of the state. Again,
this was clearly explained in the instructions. However 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 HL and 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
33
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
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.
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.
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.
34
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 0 6 0 1
Both A and B transmit 0 12 55 41 92 75
Table 3: Withholding strategies
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 HL with 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 reinforcing the
results of the Wilcoxon test.
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-
35
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
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
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.
36
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
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
37
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
(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
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.
6
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.
7
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
6
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.
7
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.
38
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
Table 7: Individuals using “approximately optimal” cutpoint strategies
two-thirds of all cases (95 out of 144), which reinforces our previous conclusion that
subjects play this game rather well.
Finally, in Figure 5 we look at each individual (ordered by their ID number) and
determine 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. So, 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 evi-
dence. 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 Media outlet i 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
39
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.
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.
8
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.
9
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.
10
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:
11
?
integraldisplay
100
0
(s?50)
2
40
1
100
ds = ?20.83
8
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).
9
This extremely low proportion of mistakes is consistent with the behavior in sessions 1 and 2
of experiment 1.
10
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.
11
Recall that C players get a fixed 120 points in each match to which the costs of actions and
viewing decisions are subtracted.
40
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
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.
12
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.
13
This is in
12
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”.
13
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 obtaining no transmission or after obtaining the information,
but in line with a rational choice, we strongly suspect that it is the former.
41
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.
Decisions viewed
0 1 2
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
42
(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
(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
43
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.
# 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
44
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.
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.
45
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)
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.
46
Overall, players do understand the reputation effect: player C 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
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 provide more infor-
mation 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
47
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
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 .
48
It would be helpful to further 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
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 may want to have
more observations. These considerations will be the object of future work.
49
1 
 
APPENDIX A ? FIGURES 
 
Figure 1 ? Distribution of behavior of Roles A and B in LL. 
 
 
Figure 2 ? Distribution of behavior of Roles A and B in HL. 
2 
 
 
Figure 3 ? Distribution of behavior of Roles A and B in HH. 
 
 
Figure 4 ? Cumulative distribution functions of C's action. 
 
3 
 
 
Figure 5 – Number of mistakes by individual under Roles A and B 
 
 
 
Figure 6 – Distribution of behavior of Roles A and B in groups of 5 with low costs. 
4 
 
 
 
Figure 7 – Distribution of behavior of Roles A and B in groups of 5 with high costs. 
 
 
 
Figure 8 – Distribution of behavior of Roles A and B in group of 7 with low costs. 
5 
 
 
 
 
Figure 9 – Distribution of behavior of Roles A and B in group of 7 with high costs. 
 
 
Figure 10 – Decisions viewed and information transmitted in Group 2, state A. 
6 
 
 
Figure 11 – Decisions viewed and information transmitted in Group 2, state B. 
 
 
 
 
 
Figure 12 – Decisions viewed and information transmitted in Group 3, state A. 
 
 
7 
 
 
 
Figure 13 – Decisions viewed and information transmitted in Group 3, state B. 
 
 
 
Figure 14 – Decisions viewed and information transmitted in Group 4, state A. 
 
. 
8 
 
 
Figure 15 – Decisions viewed and information transmitted in Group 4, state B. 
 
 
 
 
 
 
1 
 
APPENDIX B  –  INSTRUCTIONS  
 
FCC -- EXPERIMENT  1  –  INSTRUCTIONS   –  01.16.2011 
 
 Thank you for agreeing to participate in this research experiment on group decision making. 
During the experiment we would like to have your undistracted attention.  Do not open other 
applications on your computer, chat with other students, use your phone or headphones, etc.   
 
For your participation, you will be paid in cash from a research grant, at the end of the 
experiment.  Different participants may earn different 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 carefully, and fully understand the instructions. You will be asked some review questions after 
the instructions, which you will have to answer correctly 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 will take place through computer terminals. All interaction between 
you and other participants will take place through the computer interface. It is important that you not 
try to communicate with other participants during the experiment, except according to the rules 
described in the instructions. 
  
We will start with a brief instruction period.  During this instruction period, you will be given 
a complete description of the experiment and will be shown how to use the computer. At the end of 
the session, you will be paid the sum of what you have earned in all matches. Everyone will be paid 
in private and you are under no obligation to tell others how much you earned. Your earnings during 
the experiment are denominated in points. At the end of the experiment you will be paid $1.00 for 
every _160_ points you have earned. 
 
 The experiment will consist of several matches. In each match, you will be grouped with two 
other participants in the experiment. Since there are ____ participants in today’s session, there will be 
____ groups of 3 in each match. You are not told the identity of the participants you are grouped with. 
Your payoff depends only on your decision and the decisions of the two participants you are grouped 
with. What happens in the other groups has no effect on your payoff and vice versa. Your decisions 
are not revealed to participants in the other groups. 
 
 In each match, you will 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 screen. The computer will also draw one 
number between 0 and 100 and all numbers are equally likely.  This number is called the state. 
 
What to do 
 
If you have Role A, the computer will disclose the state to you. You will then have to 
“Transmit” the state or “Withhold” the state. If you choose to “Withhold” the state, you will pay a 
cost. If you choose to “Transmit” the state you will not pay any cost. 
 
If you have Role B, the same options are offered to you except that the cost if you choose to 
“Withhold” the state may be different. Both costs will be clearly displayed on your screen. Last, you 
will not be able to see the decision of the participant in the other role when you make your decision. 
After choosing “Transmit” or “Withhold”, you will be instructed to wait. 
2 
 
 
If you have Role C, you will be instructed to wait until the two other participants have each 
chosen to “Transmit” or “Withhold” the state. Then, the computer will display the cost of withholding 
for the participants with roles A and B. The computer will also display the state if both roles A and B 
choose to “Transmit” the state. If at least one of them chooses to “Withhold” the state, the computer 
will report that the state is “unknown”. In either case, you will be prompted to select your action 
which consists of a number between 0 and 100. 
 
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 see the payoff of all the participants in the group.  
 
When all groups have finished the match and have seen the results, we proceed to the next 
match. For the next match, the computer randomly reassigns all participants to new groups. In each 
group, the computer assigns new roles, and randomly selects a new state between 0 and 100. The new 
assignments do not depend in any way on the past decisions of any participant including you and are 
done completely randomly by the computer. The assignments are independent across groups, across 
participants, and across matches. This next match then follows the same rules as the previous match. 
 
How much you get 
 
If your role is A, your payoff is the action selected by C minus the cost if you withheld the 
state. Therefore, A wants C to choose an action as high as possible. 
 
If your role is B, your payoff is 100 minus the action selected by C minus the cost if you 
withheld the state. Therefore, B wants C to choose an action as low as possible. 
 
If you have Role C, your payoff 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 choose an action that equals your expectation 
regarding the state. To see this, suppose 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 choose action 20 or 40, your payoff is 95 
Instead, if you choose 30 (that is, 20*0.5 + 40*0.5), your payoff is 97.5. 
 
Finally, if you know the state for sure, then you should choose your action equal to the state and 
obtain a payoff of 100 for sure. 
 
There will be one practice match. The points accumulated in this match do not count towards 
your final dollar earnings. The practice match is similar to the matches in the experiment.  
 
Before the practice match, we will present the game using screenshots. It is important that 
you understand this information. If you have a question during this presentation, raise your hand and 
we will answer you. 
3 
 
 
Display 1. Sample screenshot for roles A and B 
 
If you have either Role A or Role B, you will see a screen similar to this: 
 
Your Role is displayed at the top of the screen. In that example, you have Role A. In that 
match, the state is 57. Your cost of withholding the state is 40 and the cost of withholding of the 
participant with role B is 0. If you want to Transmit, you have to click the “Transmit” button. If you 
want to “Withhold”, you have to click the “Withhold” button. 
 
Display 2. Sample screenshot for role C 
 
If you have Role C, you will see a screen similar to this after A and B have made their choices: 
 
The costs of withholding 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 “withhold” the state. You must choose your action by entering 
a number between 0 and 100 in the box and click “Submit”. 
 
4 
 
Display 3. Sample screenshot of the last screen 
 
This is the last screen you see in the match.  
 
 
Participants in all three roles A, B and C see the exact same screen, except for the top line 
that displays your role and the bottom history lines. In that example, the state was 63 and C selected 
action 88. 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 payoffs correspond to a different 
match than the one in displays 1 and 2 and it is presented only for illustration. 
 
At the bottom of the screen, the history of previous matches is displayed. For each match, the 
screen shows the state, the decision of roles A and B (transmit or withhold) and the action of role C 
(number between 0 and 100). It also shows your own role and the payoff you obtained. To reach the 
next match, you need to click “Continue”. 
 
Recap 
  Here is a brief recap of the important things you will see, and how they affect your payoffs: 
 
(1) Roles A and B know the state. Each chooses whether to “Transmit” or to “Withhold” the 
state. The decisions to “Withhold” 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 chooses to “Withhold” the state. 
(3) The payoff for A is the action of C minus the cost if A withheld the state. The payoff for B is 
100 minus the action of C minus the cost if B withheld the state. 
(4) The payoff 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?   
5 
 
[PAUSE to answer questions] 
 
------------------------------------------------------------------ 
 
We will now begin the Practice session 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 will have to answer 
some review questions. Everyone must answer all the questions correctly 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 see the first screen 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 CORRECT SCREEN] 
 
At the top left of the screen you see your subject ID. Please record that on your record sheet 
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 screen looks similar to the screenshot in display 1. If you have Role C, you are instructed 
to wait. In both cases, at the bottom of the screen you can see a history panel with all the information 
relevant for each match. 
 
 If you have Role A or Role B and your subject ID is even, click on the “Transmit” button. 
Otherwise, click on the “Withhold” button.  Note that it does not matter which one you choose since 
you will not be paid for this match. 
 
If you have Role C, you should now see a screen similar to the screenshot 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 matter 
which number you type since you will not be paid for this match. 
 
You should now all see a screen similar to the one in display 3. It displays the state, the action 
of C and the payoffs of all participants in your group. 
 
Now click “Continue”. The practice match is over. Please complete the review questions 
before we begin the paid session. Once you answer all the questions correctly, click submit. After all 
participants in your group have answered all questions correctly, the quiz will disappear from your 
screen. Raise your hand if you have any question. 
 
[WAIT FOR EVERYONE TO FINISH THE QUIZ] 
 
6 
 
Are there any questions before we begin with the paid session?  
 
We will now begin with the paid matches. If there are any problems or questions from this 
point on, raise your hand and an experimenter will come and assist you.  
 
For the next matches the cost of withholding for Role A is ___ and for Role B is ___.   
 
[at the end of GAME ____] 
 
For the next ___ matches the cost of withholding 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 withholding 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 will be paid the payoff you have accumulated 
in the ____ paid matches. The payoff appears on your screen. Please write this payoff in your record 
sheet and remember to CLICK OK after you are done. 
 
[CLICK ON WRITE OUTPUT] 
 
We will now pay each of you in private in the next room 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 call you to be paid. Do not converse with the other participants or use 
your cell phone. Thank you for your cooperation. 
  
[CALL all the participants in sequence by their ID #] 
 
[Note to experimenter: use the “pay” file to call and pay subjects] 
 
Could the person with ID number 1 go to the next room to be paid?  
 
 
7 
 
RECORD SHEET 
 
 
 
 
Subject ID:           ___________ 
 
 
TOTAL EARNINGS:         $______ 
 
 
 
 
 
 
Name:________________________   Date:________________________ 
 
  Amount received:______________ 
 
School ID #:___________________   Signature:_____________________ 
 
 
 
 
 
  
8 
 
FCC – EXPERIMENT 2 (groups of 5) – INSTRUCTIONS  – 01.17.2011 
 
 Thank you for agreeing to participate in this research experiment on group decision making. 
During the experiment we would like to have your undistracted attention.  Do not open other 
applications on your computer, chat with other students, use your phone or headphones, read, etc.   
 
For your participation, you will be paid in cash from a research grant, at the end of the 
experiment.  Different participants may earn different 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 carefully, and fully understand the instructions. You will be asked some review questions after 
the instructions, which you will have to answer correctly 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 will take place through computer terminals. All interaction between 
you and other participants will take place through the computer interface.  It is important that you not 
try to communicate with other participants during the experiment, except according to the rules 
described in the instructions. 
  
We will start with a brief instruction period.  During this instruction period, you will be given 
a complete description of the experiment and will be shown how to use the computers.  At the end of 
the session, you will be paid the sum of what you have earned in all matches. Everyone will be paid 
in private and you are under no obligation to tell others how much you earned. Your earnings during 
the experiment are denominated in points. At the end of the experiment you will be paid $1.00 for 
every _160_ points you have earned. 
 
 At the beginning of the experiment, you will be grouped with four other participants. Since 
there are ____ subjects in today’s session, there will be ____ groups of five. You are not told the 
identity of the participants you are grouped with. Your payoff depends only on your decision and the 
decisions of the participants you are grouped with. What happens in the other groups has no effect on 
your payoff and vice versa. Your decisions are not revealed to participants in the other groups. 
 
 In each group, there will be three types of roles, Role A, Role B and Role C. There will be 
two participants in Role A, called A1, A2 participants, two participants in Role B, called B1, B2 
participants and one participant in Role C, called C participant. You will have either role A, role B or 
role C. Which role you have is randomly selected at the beginning of the experiment and is clearly 
displayed on the screen. You will keep the same role and will be in the same group with the same 
participants for the entire duration of the experiment.  
 
The experiment will consist of several matches. In each match, the computer will draw two 
numbers. Each of these numbers can be any number between 0 and 100 and all numbers are equally 
likely. These numbers are called state A and state B. 
 
What to do 
 
If your role is A1 or A2 (you are an A participant) the computer will disclose state A to you 
but not state B. Similarly, if your role is B1 or B2 (you are a B participant) the computer will disclose 
state B to you but not state A.  All A participants see the same state A, and all B participants see the 
same state B. You will then have to choose whether to “Transmit” or “Withhold” the state.  You will 
9 
 
not see the decision selected by any of the other A or B participants when you make your decision. 
You will then be instructed to wait. 
 
If you are a C participant, you will be instructed to wait until all A and B participants have 
each chosen an action (“Transmit” or “Withhold”). Then, you will see four buttons that hide the 
decision of each A and B participant.  
 
You will first have the possibility to view the decision of each A participant. If you click on 
one of the A buttons (A1 or A2), the computer will reveal state A if that A participant chose 
“Transmit” and state “unknown” if that A participant chose “Withhold”. 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 choose to view 
the decision of one A participant, it is also your choice whether to view the decision of A1 or A2. 
Finally, 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 between 0 and 100. You 
then need to click “Submit”.  
 
You will then repeat the same steps regarding B participants. The only difference is that the 
costs of viewing the decisions of the B participants are different, 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 between 0 and 100. You then need 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 see the payoffs of 
all the participants in the group.  
 
When all groups have finished the match and have seen the results, we proceed to the next 
match. For the next match, the computer randomly selects two new numbers between 0 and 100 
which correspond to the new states A and B. In the new match, you will be in the same group with the 
same participants and you will keep the same Role. Also, at the bottom of the screen you will see a 
History summarizing what has happened in the past matches of your group: which A and B 
participants chose to transmit and which ones chose to withhold, 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 payoff is 50 plus the difference between 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), (ii) to choose an action A as high as possible, and (iii) to 
choose an action B as low as possible. 
 
If you are a B participant, your payoff is 50 plus the difference between 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), (ii) to choose an action B as high as possible, and (iii) to 
choose an action A as low as possible. 
 
If you are a C participant, your payoff 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:  
 
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 choose each action equal to the expected value 
of the corresponding state. To see this, suppose for simplicity there is only state A, and suppose 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 choose action 20 or 40, your payoff is 115 – cost of viewing As and Bs decisions. 
Instead, if you choose 30 (that is, 20*0.5 + 40*0.5), your payoff is 117.5 – cost of viewing As and Bs 
decisions.  Naturally, if you know one of the states for sure, then you should choose the action for that 
state equal to the state. 
 
The cost of viewing the decisions of A and B participants are as follows. 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 
will be reversed, and will be clearly explained when we reach that stage.   
 
There will be one practice match. The points accumulated in this match do not count towards 
your final dollar earnings. The practice match is similar to the matches in the experiment.  
 
Before the practice match, we will present the game using screenshots. It is important that 
you understand this information. If you have a question during this presentation, raise your hand and 
we will answer you.  
 
Display 1. Sample screenshot for A and B participants 
This screen is displayed to you if you are either an A or a B participant. The exact Role is displayed at 
the top of the screen. In that example, you are participant B1. 
 
  
In that match, state B is 85. You have to choose between “Transmit” or “Withhold” the state. You 
simply need to click the corresponding button. 
11 
 
 
Display 2. First sample screenshot for C participant 
This screen is displayed to you if you have Role C and after all A and B participants have made their 
decisions. 
 
You have the possibility 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 buttons to view the decisions of B 
participants, but they are disabled at this point. 
 
Display 3. Second sample screenshot for C participant 
 
This screen is the second screen you see when you have Role C. Once you have submitted your 
decision regarding state A, the buttons to view the decisions of A participants are disabled. The 
number you submitted is also visible but you cannot change it anymore.    
 
In this example, you viewed the decision of A1 who transmitted the state, so you learned that 
state A was 84. You also viewed the decision of A2 who chose to withhold the information. Finally, 
12 
 
you chose action 99. Note that this is an illustration: the decisions and numbers only reflect a 
randomly generated behavior. 
 
Now, you have the possibility to view the decisions of B1 and B2. Last, you must enter a 
number in the box and click “Submit”. 
 
Display 4. Sample screenshot of the last screen 
 
This is the last screen you see in the match. All participants see the exact same screen, except for the 
top line that displays only your role.  
 
 
The screen shows the states A and B, the actions A and B chosen by the C participant and the payoffs 
of all participants in the group. To reach the next match, you need to click “Continue”. 
 
Notice that at the bottom of the screen, you can also see the history of previous matches. For each 
match, the screen 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 screen is important as it tracks the past behavior of each participant. 
 
Recap 
 
 Here is a brief recap of the important things you will see, and how they affect your payoffs: 
 
(1) Roles A know state A and can choose to “Transmit” or “Withhold” it to C. Similarly, Roles B 
know state B and can choose to “Transmit” or “Withhold” it to C. 
(2) If C clicks on a participant’s button, C will learn the state if that participant chose “Transmit” 
and he will see “unknown” if that participant chose “Withhold”. Clicking on a participant’s 
button is costly.  
(3) The payoff of an A participant is 50 + action A – action B + 20 
 
if C views your decision. The 
payoff 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. 
13 
 
(4) The payoff 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?   
 
14 
 
 
  RECORD SHEET 
 
 
 
 
Subject ID:           ___________ 
 
 
  
 
TOTAL EARNINGS:         $______ 
 
 
 
 
 
 
Name:________________________   Date:________________________ 
 
  Amount received:______________ 
 
School ID #:___________________   Signature:_____________________ 
 
 
 
 
 
 
 
 
 
15 
 
[THE NEXT PAGE ONLY FOR THE EXPERIMENTER] 
 
[PAUSE to answer questions] 
 
------------------------------------------------------------------ 
 
We will now begin the Practice session 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 will have to answer 
some review questions. Everyone must answer all the questions correctly 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 see the first screen 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 CORRECT SCREEN] 
 
At the top left of the screen you see your subject ID. Please record that on your record sheet 
now. Some of you have Role A, some have Role B and some have Role C. If you have Role A or B, 
the screen looks similar to the screenshot in display 1. If you have Role C, you are instructed to wait. 
In all cases, at the bottom of the screen you can see a history panel with all the information relevant 
for each match. 
 
 If you have Role A or B, and your subject ID is even, click on the “Transmit” button. If it is 
odd, click on the “Withhold” button. Note that it does not matter which one you choose since you will 
not be paid for this match. 
 
If you have Role C, you should now see a screen similar to the screenshot in display 2. If you 
have Roles A or B, you are instructed to wait.  Click on the buttons to see 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 see a screen similar to the screenshot in display 3. If you 
have Roles A or B, you are instructed to wait. Click on the buttons to see B2 and B3’s decisions. 
Now, type the last two digits of your year of birth and click “Submit”. 
 
You should now all see a screen similar to the one in display 4. It displays the states, the 
actions of C and the payoffs of all participants in your group. 
 
Now click “Continue”. The practice match is over. Please complete the review questions 
before we begin the paid session. Once you answer all the questions correctly, click submit. After all 
participants in your group have answered all questions correctly, the quiz will disappear from your 
screen. Raise your hand if you have any question. 
16 
 
 
[WAIT FOR EVERYONE TO FINISH THE QUIZ] 
 
Are there any questions before we begin with the paid session?  
 
We will 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 follows. 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 will be paid the payoff you have accumulated 
in the ____ paid matches. The payoff appears on your screen. Please write this payoff in your record 
sheet and remember to CLICK OK after you are done. 
 
[CLICK ON WRITE OUTPUT] 
 
We will now pay each of you in private in the next room 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 call you to be paid. Do not converse with the other participants or use 
your cell phone. Thank you for your cooperation. 
  
[CALL all the participants in sequence by their ID #] 
 
[Note to experimenter: use the “pay” file to call and pay subjects] 
 
Could the person with ID number 1 go to the next room to be paid?  
 
17 
 
FCC – EXPERIMENT 2 (groups of 7) – INSTRUCTIONS – 01.17.2011 
 
 Thank you for agreeing to participate in this research experiment on group decision making. 
During the experiment we would like to have your undistracted attention.  Do not open other 
applications on your computer, chat with other students, use your phone or headphones, read, etc.   
 
For your participation, you will be paid in cash from a research grant, at the end of the 
experiment.  Different participants may earn different 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 carefully, and fully understand the instructions. You will be asked some review questions after 
the instructions, which you will have to answer correctly 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 will take place through computer terminals. All interaction between 
you and other participants will take place through the computer interface.  It is important that you not 
try to communicate with other participants during the experiment, except according to the rules 
described in the instructions. 
  
We will start with a brief instruction period.  During this instruction period, you will be given 
a complete description of the experiment and will be shown how to use the computers.  At the end of 
the session, you will be paid the sum of what you have earned in all matches. Everyone will be paid 
in private and you are under no obligation to tell others how much you earned. Your earnings during 
the experiment are denominated in points. At the end of the experiment you will be paid $1.00 for 
every _160_ points you have earned. 
 
 At the beginning of the experiment, you will be grouped with six other participants. Since 
there are ____ subjects in today’s session, there will be ____ groups of seven. You are not told the 
identity of the participants you are grouped with. Your payoff depends only on your decision and the 
decisions of the participants you are grouped with. What happens in the other groups has no effect on 
your payoff and vice versa. Your decisions are not revealed to participants in the other groups. 
 
 In each group, there will be three types of roles, Role A, Role B and Role C. There will be 
three participants in Role A, called A1, A2, A3 participants, three participants in Role B, called B1, 
B2, B3 participants and one participant in Role C, called C participant. You will have either role A, 
role B or role C. Which role you have is randomly selected at the beginning of the experiment and is 
clearly displayed on the screen. You will keep the same role and will be in the same group with the 
same participants for the entire duration of the experiment.  
 
The experiment will consist of several matches. In each match, the computer will draw two 
numbers. Each of these numbers can be any number between 0 and 100 and all numbers are equally 
likely. These numbers are called state A and state B. 
 
What to do 
 
If your role is A1, A2 or A3 (you are an A participant) the computer will 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 will 
disclose state B to you but not state A.  All A participants see the same state A, and all B participants 
see the same state B. You will then have to choose whether to “Transmit” or “Withhold” the state.  
18 
 
You will not see the decision selected by any of the other A or B participants when you make your 
decision. You will then be instructed to wait. 
 
If you are a C participant, you will be instructed to wait until all A and B participants have 
each chosen an action (“Transmit” or “Withhold”). Then, you will see six buttons that hide the 
decision of each A and B participant.  
 
You will first have the possibility to view the decision of each A participant. If you click on 
one of the A buttons (A1, A2 or A3), the computer will reveal state A if that A participant chose 
“Transmit” and state “unknown” if that A participant chose “Withhold”. 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 choose to 
view the decision of one A participant, it is also your choice whether to view the decision of A1, A2 
or A3. Finally, 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 between 0 and 
100. You then need to click “Submit”.  
 
You will then repeat the same steps regarding B participants. The only difference is that the 
costs of viewing the decisions of the B participants are different, 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 between 0 and 100. You then need 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 see the payoffs of 
all the participants in the group.  
 
When all groups have finished the match and have seen the results, we proceed to the next 
match. For the next match, the computer randomly selects two new numbers between 0 and 100 
which correspond to the new states A and B. In the new match, you will be in the same group with the 
same participants and you will keep the same Role. Also, at the bottom of the screen you will see a 
History summarizing what has happened in the past matches of your group: which A and B 
participants chose to transmit and which ones chose to withhold, 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 payoff is 50 plus the difference between 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), (ii) to choose an action A as high as possible, and (iii) to 
choose an action B as low as possible. 
 
If you are a B participant, your payoff is 50 plus the difference between 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), (ii) to choose an action B as high as possible, and (iii) to 
choose an action A as low as possible. 
 
If you are a C participant, your payoff 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:  
 
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 choose each action equal to the expected value 
of the corresponding state. To see this, suppose for simplicity there is only state A, and suppose 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 choose action 20 or 40, your payoff is 115 – cost of viewing As and Bs decisions. 
Instead, if you choose 30 (that is, 20*0.5 + 40*0.5), your payoff is 117.5 – cost of viewing As and Bs 
decisions.  Naturally, if you know one of the states for sure, then you should choose the action for that 
state equal to the state. 
 
The cost of viewing the decisions of A and B participants are as follows. 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 cannot view the decision of all three 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 cannot view the decision of all three B participants. The costs in the 
second part of the experiment will be reversed, and will be clearly explained when we reach that 
stage.   
 
There will be one practice match. The points accumulated in this match do not count towards 
your final dollar earnings. The practice match is similar to the matches in the experiment.  
 
Before the practice match, we will present the game using screenshots. It is important that 
you understand this information. If you have a question during this presentation, raise your hand and 
we will answer you.  
 
Display 1. Sample screenshot for A and B participants 
This screen is displayed to you if you are either an A or a B participant. The exact Role is displayed at 
the top of the screen. In that example, you are participant B1. 
 
20 
 
  
In that match, state B is 19. You have to choose between “Transmit” or “Withhold” the state. You 
simply need to click the corresponding button. 
 
Display 2. First sample screenshot for C participant 
This screen is displayed to you if you have Role C and after all A and B participants have made their 
decisions. 
 
You have the possibility 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 buttons to view the decisions of B 
participants, but they are disabled at this point. 
 
Display 3. Second sample screenshot for C participant 
 
This screen is the second screen you see when you have Role C. Once you have submitted your 
decision regarding state A, the buttons to view the decisions of A participants are disabled. The 
number you submitted is also visible but you cannot change it anymore.    
 
21 
 
In this example, you viewed the decision of A1 who transmitted the state, so you learned that 
state A was 61. You also viewed the decision of A2 who chose to withhold the information. Finally, 
you chose action 99. Note that this is an illustration: the decisions and numbers only reflect a 
randomly generated behavior. 
 
Now, you have the possibility to view the decisions of B1, B2 and B3. Last, you must enter a 
number in the box and click “Submit”. 
 
Display 4. Sample screenshot of the last screen 
 
This is the last screen you see in the match. All participants see the exact same screen, except for the 
top line that displays only your role.  
 
 
The screen shows the states A and B, the actions A and B chosen by the C participant and the payoffs 
of all participants in the group. To reach the next match, you need to click “Continue”. 
 
Notice that at the bottom of the screen, you can also see the history of previous matches. For each 
match, the screen 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 screen is important as it tracks the past behavior of each participant. 
 
Recap 
 
 Here is a brief recap of the important things you will see, and how they affect your payoffs: 
 
(1) Roles A know state A and can choose to “Transmit” or “Withhold” it to C. Similarly, Roles B 
know state B and can choose to “Transmit” or “Withhold” it to C. 
(2) If C clicks on a participant’s button, C will learn the state if that participant chose “Transmit” 
and he will see “unknown” if that participant chose “Withhold”. Clicking on a participant’s 
button is costly.  
22 
 
(3) The payoff of an A participant is 50 + action A – action B + 20 
 
if C views your decision. The 
payoff 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 payoff 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?   
 
23 
 
 
  RECORD SHEET 
 
 
 
 
Subject ID:           ___________ 
 
 
  
 
TOTAL EARNINGS:         $______ 
 
 
 
 
 
 
Name:________________________   Date:________________________ 
 
  Amount received:______________ 
 
School ID #:___________________   Signature:_____________________ 
 
 
 
 
 
 
 
 
 
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[THE NEXT PAGE ONLY FOR THE EXPERIMENTER] 
 
[PAUSE to answer questions] 
 
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We will now begin the Practice session 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 will have to answer 
some review questions. Everyone must answer all the questions correctly 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 see the first screen 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 CORRECT SCREEN] 
 
At the top left of the screen you see your subject ID. Please record that on your record sheet 
now. Some of you have Role A, some have Role B and some have Role C. If you have Role A or B, 
the screen looks similar to the screenshot in display 1. If you have Role C, you are instructed to wait. 
In all cases, at the bottom of the screen you can see a history panel with all the information relevant 
for each match. 
 
 If you have Role A or B, and your subject ID is even, click on the “Transmit” button. If it is 
odd, click on the “Withhold” button. Note that it does not matter which one you choose since you will 
not be paid for this match. 
 
If you have Role C, you should now see a screen similar to the screenshot in display 2. If you 
have Roles A or B, you are instructed to wait.  Click on the buttons to see 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 see a screen similar to the screenshot in display 3. If you 
have Roles A or B, you are instructed to wait. Click on the buttons to see B2 and B3’s decisions. 
Notice that once you have seen the decisions of two B participants you cannot click on the 
decision of the third. Now, type the last two digits of your year of birth and click “Submit”. 
 
You should now all see a screen similar to the one in display 4. It displays the states, the 
actions of C and the payoffs of all participants in your group. 
 
Now click “Continue”. The practice match is over. Please complete the review questions 
before we begin the paid session. Once you answer all the questions correctly, click submit. After all 
25 
 
participants in your group have answered all questions correctly, the quiz will disappear from your 
screen. 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 session?  
 
We will 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 follows. 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 cannot view the decision of all three A 
participants or all three 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 cannot view the decision of all three A participants or all three B 
participants. 
 
[at the end of GAME ____] 
 
This was the last match of the experiment. You will be paid the payoff you have accumulated 
in the ____ paid matches. The payoff appears on your screen. Please write this payoff in your record 
sheet and remember to CLICK OK after you are done. 
 
[CLICK ON WRITE OUTPUT] 
 
We will now pay each of you in private in the next room 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 call you to be paid. Do not converse with the other participants or use 
your cell phone. Thank you for your cooperation. 
  
[CALL all the participants in sequence by their ID #] 
 
[Note to experimenter: use the “pay” file to call and pay subjects] 
 
Could the person with ID number 1 go to the next room to be paid?