Ohio State University Team versus Individual Play Summary 1. The summaries must at least be one full page (no more than two pages)2. Summarize the major po

Ohio State University Team versus Individual Play Summary 1. The summaries must at least be one full page (no more than two pages)2. Summarize the major points of the reading.3. Provide some of your opinion about the paper and any questions you might have. Are Two Heads Better than One?
Team versus Individual Play in Signaling Games*
David J. Cooper
Department of Economics
Weatherhead School of Management
Case Western Reserve University
John H. Kagel
Department of Economics
Ohio State University
December 22, 2004
Abstract: We compare individuals with two-person teams in signaling game experiments. Teams
consistently play more strategically than individuals, and generate positive synergies in more
difficult games, beating a demanding “truth wins” norm. The superior performance of teams is
most striking following changes in payoffs that change the equilibrium outcome. Individuals
play less strategically following the change in payoffs than inexperienced subjects playing the
same game. In contrast, the teams exhibit positive learning transfer, playing more strategically
following the change than inexperienced subjects. Dialogues between teammates are used to
identify factors promoting strategic play.
Key words: teams, signaling games, learning transfer
JEL classification: C72, C92, D82, L12.
* Research support from the National Science Foundation (SBR-9809538) is gratefully
acknowledged. Helpful research assistance was provided by Alex Brown, Bethia Cullis,
Guillaume Frechette, John Lightle, and Todd Schoellman. We have received helpful comments
from Eric Bettinger, John Ham, David Laibson, James Peck, Alvin Roth, seminar participants at
Carnegie-Mellon University, Emory University, Harvard University, Ohio State University,
University College London, and University of Wyoming as well as the referees and editor of this
journal. Any opinions, findings, and conclusions or recommendations in this material are those
of the authors and do not necessarily reflect the views of the National Science Foundation.
Many economic decisions are made within a team or group framework with two or more
economic agents consulting with each other in deciding what course of action to take. For
example, corporate bid teams, often in conjunction with outside consultants, determined bidding
strategies in the spectrum (air wave) rights auctions. U.S. monetary policy is determined by the
twelve member Open Market Committee of the Federal Reserve Bank. More generally, virtually
all significant strategic decisions by corporations are made within a group or team framework.
In contrast, much of economic theory and game theory, and most experimental investigations of
these theories, make no distinction between strategic decisions made by teams versus
individuals. As a result there is, potentially, a significant hole in our understanding of large areas
of economic behavior. If there are major differences between individuals and teams in important
economic settings, direct extrapolation of individual level research to team performance may be
strikingly inconsistent with observed behavior. The results presented here, which find
substantial differences between the behavior of individuals and teams in signaling games,
indicate these concerns are likely to be well founded.
We report experiments comparing the behavior of individuals versus freely interacting twoperson teams in Paul Milgrom and John R. Roberts’ (1982) entry limit pricing game. Strategic
play in this game revolves around an incumbent monopolist attempting to deter entry by
signaling it will be a tough competitor for a potential entrant. Specifically, strategic play takes
place through limit pricing, the choice by incumbents of greater quantities (and lower prices by
extension) than would prevail in the absence of asymmetric information. Past experiments with
signaling games shows that equilibrium play emerges only gradually, requiring a number of
replications of the game before anything approaching an equilibrium emerges (Jordi Brandts and
Charles A. Holt, 1992; David J. Cooper, Susan Garvin and John H. Kagel, 1997a; Cooper,
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Kagel, Wei Lo, and Qing Liang Gu, 1999).
We study three different versions of the limit pricing game which vary in the difficulty of
learning to play strategically. We focus on how fast strategic play (e.g. limit pricing) develops
for teams versus individuals, as well as identifying possible qualitative differences in the
learning/adjustment process between teams and individuals. For all three treatments the
equilibrium towards which play converges is the same for teams and individuals, but teams learn
to play strategically faster than individuals. Impressively, in the more difficult games teams beat
a demanding “truth wins” norm drawn from the psychology literature.
The differences between teams and individuals are most striking following changes in
payoffs that affect the equilibrium outcome. In this cross-over treatment, subjects first play a
game that supports both pure strategy pooling and separating equilibria, with play converging on
a pooling equilibrium, and are then switched to a game in which the only pure strategy equilibria
are separating. For individuals, experience in the game with pooling equilibria retards
adjustment to the separating equilibria following the change in games (compared to individuals
who play the same game but with no prior experience), so that there is negative learning transfer
between games. However, for teams, experience in the game with pooling equilibria enhances
adjustment to the separating equilibrium (compared to teams with no previous experience),
yielding positive learning transfer between games. Thus, teams not only learn to play
strategically faster than individuals but also follow a different learning/adjustment process than
individuals.
An important methodological innovation of our procedures is the recording and coding of
dialogues between teammates as they coordinate their decisions. These dialogues provide a
direct window into teams’ learning processes. Analysis of the dialogues indicates that a critical
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step in monopolists’ learning to play strategically is putting themselves in the entrant’s shoes,
reasoning from the entrant’s point of view to infer likely responses to their choice as a
monopolist. Statements to this effect are (i) among the most commonly coded statements prior
to limit pricing, (ii) among the best predictors of whether teams will continue to limit price after
their first attempt to do so, and (iii) are much more common immediately following the change
in payoffs in the cross-over treatment compared to inexperienced teams playing the same game.
Thus, the kind of interactive reasoning that underlies much of game theory has clear empirical
validity in our data.
Beyond the importance of our results for economics and game theory, our work also speaks
to the large psychology literature on group decision making by consciously “common-purpose”
groups seeking consensus on how to solve a specific problem. There are two distinct branches to
this literature, one dealing with judgmental questions and another dealing with “eureka” type
problems requiring no special information to solve, but having solutions that tend to be selfconfirming if discovered. The latter is closest in spirit to our game. For such problems
psychologists apply a “truth wins” norm in judging whether or not teams are superior to
individuals. Intuitively, a team should be no less likely to solve a problem than its most able
member would be acting alone. By comparing the performance of freely interacting teams with
this norm, psychologists identify the presence of positive, negative, or zero synergies for teams.
The rich psychology literature on team versus individual play in eureka problems
consistently finds that teams typically fall well short of the truth wins norm (James H. Davis,
1992). In contrast, for two out of our three treatments teams meet or beat the truth wins norm,
indicating strong positive synergies from the teams treatment. The concluding section of the
paper identifies important differences in experimental procedures, and between games with
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strategic interactions like we study versus games against nature that psychologists typically
study, that likely account for the striking differences between our results and those in the
psychology literature. We also compare our results to the limited literature on team versus
individual play previously reported in the economics literature.
The paper proceeds as follows: Section I characterizes the structure of the limit-pricing game
and the equilibria for the games played. Section II defines what we mean by strategic play and
relates learning to play strategically in our experiment to the truth wins norm. Section III
outlines our experimental procedures. Results are reported in Section IV. Section V reports on
the team dialogues for insights into the leaning process and to fully justify our definition of
strategic play. The last section of the paper summarizes our main findings and relates our results
to the psychology and economics literatures on teams versus individuals and cross-game
learning.
I) The Limit Pricing Game: The games studied here are based on Milgrom and Roberts’ (1982)
entry limit pricing model. For our purposes, the industrial organization implications of the
model are of secondary importance. We therefore employ a very stylized version of the model,
focusing on the signaling aspects of the game.
A. Structure of the Game: The limit pricing game is played between an incumbent monopolist
(M) and a potential entrant (E). The game proceeds as follows: (1) M observes its type, high
cost (MH) or low cost (ML). The two types are realized with equal probability with this being
common knowledge. (2) M chooses one of seven output levels. M’s payoff, shown in Table 1a,
is contingent on its type, the output level chosen, and E’s response. (3) E sees M’s output, but
not M’s type, and either plays IN or OUT. The asymmetric information, in conjunction with the
fact that it is profitable to enter against MHs, but not against MLs, provides an incentive for
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strategic play (limit pricing) by Ms. E’s payoff depends on M’s type and on E’s decision, not
on M’s choice. As a treatment variable, two different payoff tables, Tables 1b and 1c, were used
for Es. These represent “high cost” and “low cost” Es respectively. Only one of these tables
was in use at any given time.1
[Insert Table 1 here]
Three features of Table 1a capture the main strategic elements confronting Ms. First, all else
being equal, Ms are better off if Es choose OUT rather than IN. Second, reflecting their lower
marginal costs, MLs generally prefer higher outputs than MHs. This can be seen in Ms’ payoffs
should they ignore the effect of their choices on E’s behavior — MLs would choose 4 as opposed
to 2 for MHs. We refer to choice of 2 by MHs or 4 by MLs as the “mypopic maxima.” Third, 6
and 7 are dominated strategies for MHs, but not for MLs. At these outputs MLs can, in theory,
perfectly distinguish themselves from MHs.
For either the high or low cost entrant payoff table, it always pays for Es to play IN when M
is known to be an MH and OUT against an ML. However, given the prior probability of the
different M types, the expected value of OUT is greater than IN in Table 1b (250 vs. 187) and
the expected value of IN is greater than OUT in Table 1c (350 vs. 250).
B. Equilibrium Predictions: For Tables 1a and 1b (games with high cost Es), there exist multiple
pure strategy pooling, as well as separating, (sequential) equilibria. Pure strategy pooling
equilibria occur at outputs 1-5. To understand how these work, consider the pooling equilibrium
where both MHs and MLs choose 3. Given the prior probabilities over M’s type, E’s expected
value of OUT is greater than IN following a choice of 3. Sequential equilibrium puts no
1
Payoffs are given in the experimental currency “francs.” Francs were converted to dollars with one franc equal to
$.0025. Headings in Tables 1 and 2 have been changed to match the exposition in the text.
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restrictions on E’s beliefs following M’s choice of an output level that is supposed to be chosen
with zero probability in equilibrium. Therefore, it is admissible for E to believe that any
deviation from 3 involves an MH type with sufficiently high probability to induce choice of IN.
Given these beliefs and the resulting actions by Es, both MHs and MLs achieve higher profits at
3 rather than deviating to some other output level. The other pooling equilibria are constructed
in a similar fashion. The pooling equilibria at outputs 3-5 involve limit pricing by MHs choosing higher outputs (and hence lower prices) than would prevail under full information
about Ms type.
Two pure strategy separating equilibria also exist. In both of these MHs choose 2 and are
always entered on; MLs either always choose 6 or 7 and never incur entry. With MLs choosing
6 or 7, MHs cannot profitably imitate them since 2 dominates 6 and 7 for MHs. Out-ofequilibrium beliefs supporting these equilibria are that any deviation involves an MH type with
sufficiently high probability to induce entry. These separating equilibria involve limit pricing by
MLs.
For Tables 1a and 1c (the limit pricing game with low cost Es) the expected value of IN is
greater than OUT if both types choose the same output level. This destroys any pure strategy
pooling equilibrium, with the only pure strategy equilibria being the two separating equilibria
just described.
As is typical of signaling games, the limit pricing game suffers from an overabundance of
equilibria. To obtain sharper predictions, one must apply equilibrium refinements. The intuitive
criterion (In-Koo Cho and Kreps,1987) reduces the equilibria in games with high cost Es to
pooling at 4 or 5, and the efficient separating equilibrium with MLs choosing 6. For games with
low cost Es, only the efficient separating equilibrium with MLs choosing 6 survives the intuitive
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criteria.
Our experiments employ three different versions of this limit pricing game: (1) games with
only high cost Es so that both pure strategy separating and pooling equilibria exist, (2) games
with only low cost Es for which the only pure strategy equilibria are separating, and (3) a
crossover treatment in which subjects play the game with high cost Es first, in which play
reliably converges to the pooling equilibrium at 4, after which they are switched to the game
with low cost Es. This last treatment tests for learning across games.
C. Defining strategic play: In the analysis of the experimental data that follows we focus on the
development of strategic play for Ms. Strategic play is defined as MHs choice of outputs 3-5 in
games with high cost Es and MLs choice of outputs 5-7 in games with low cost Es. These are
clearly not the only possible definitions of strategic play we could employ since, in terms of the
theory, strategic play depends critically on Ms’ beliefs about Es’ responses to their actions.
However, based on the dialogues from the team treatment, and substantial circumstantial
evidence from other experiments, it is clear that Ms initial choices (which are overwhelmingly at
output 2 for MHs and 4 for MLs) involve attempts to maximize their payoffs ignoring the effect
of their choices on Es potential responses. Once Ms begin to consider the effect of their choices
on Es responses, their choices almost exclusively involve MHs choosing 3-5 in games with high
cost Es and MLs choosing 5 or 6 in games with low cost Es.
For example, consider games with high cost Es where MHs initial choices are focused on 2
for both teams and individuals (see Figures 1 and 2 reported in Section IVa below). The team
dialogues, analyzed in detail in Section V below, make it clear that MHs are essentially not
thinking about Es’ responses when making these choices. The following dialogue is a prime
example of this:
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“I think we should pick 2. What about you? It is the highest for both [meaning the highest
payoff for both choices that Es have].” [brackets added]
“I agree.”
“OK then. 2 it is.”
“It’s the highest for both.”
In the coding scheme we have developed for quantifying the dialogues between teammates,
dialogues like the preceding are coded under the category “Myopic choice as a monopolist.”
There is nothing in this dialogue (and other dialogues in the “myopic choice” category) where
MHs account for the fact that their choice will influence Es’ beliefs about their types and/or
impact on Es actions. Even though the high entry rate on 2, as compared to 3, 4 or 5, makes it
profitable for MHs to limit price from the earliest rounds of the experiments, the myopic choice
category is the second highest coded category prior to a first attempt of MH teams to play
strategically (choose 3, 4 or 5).2 In other words, MHs aren’t initially choosing 2 because they
(incorrectly) anticipate that it will lead to favorable responses by Es, but rather because they fail
to consider that their choice will impact on E’s response.
Additional circumstantial evidence pointing to the fact that initially most Ms fail to consider
Es responses to their choices comes from several sources. Most tellingly, in both earlier
experiments with the limit pricing games as well the current dataset, there are no significant
differences between MLs early plays of the game regardless of whether they faced high or low
cost Es, even though entry rates on 4 are far higher when playing against low cost Es. Further,
there is substantial evidence from a number of other experiments that subjects fail to correctly
account for their rivals actions in formulating their initial choices, and only gradually learn to do
2
The highest coded category involves taking notice of the feedback information about the population choices of Ms
as well as Es responses to same.
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so.3
II) Connections to Team Play in the Psychology and Economics Literatures
A. Connections to the psychology literature on teams: The substantial psychology literature on
team versus individual subject play distinguishes between judgmental tasks and so called
“eureka” problems.4 Judgement tasks involve settings where either there isn’t a “correct” action,
or the correct action is highly unlikely to be discovered by an untrained subject. For example,
there are numerous studies comparing the attitudes of teams and individuals towards risk. While
the choices of teams systematically differ from those of individuals, they cannot meaningfully be
termed more or less correct.5 By way of contrast, eureka problems have a correct solution (or
solutions). While this solution may be difficult to discover, it is self-confirming once discovered
and can easily be demonstrated to others. Logic problems like the Tower of Hanoi are good
examples of eureka problems. This classic puzzle, while challenging for a novice, is solved by a
simple algorithm that can be explained in a few sentences. In other words, once the puzzle has
been solved it is easy to show others that it has been successfully solved.
We argue that in signaling games, as subjects actually play the game, the discovery of
strategic play corresponds closely to solving a eureka type problem. The “aha” type insight in
signaling games is for Ms to realize that their actions affect Es’ beliefs and, by extension,
choices of Es. Once this insight has been reached, it is relatively straight forward to realize that
3
For example, in describing the failure of the intuitive criterion in signaling games, Brandts and Holt (1992, p.
1357) note that, “a type-L’s deviation to decision A might be motivated by the belief that the ‘signal,’ A or B, will
have no effect on the respondent’s decision. These beliefs are contradicted by the actual decisions of the
respondents . . .”
4
Much of our discussion of the psychology literature is based on Davis’s (1992) review article (also see Gayle W.
Hill, 1982).
5
For a general survey of the psychology literature dealing with group versus individual deci…
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