Emerging Trends in The Social and Behavioral Sciences

Against Game Theory

Item

Title

Against Game Theory

Author

Lucas, Gale M.

McCubbins, Mathew D.

Turner, Mark

Research Area

Cognition and Emotions

Topic

Decision Making

Abstract

People make choices. Often, the outcome depends on choices other people make. What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers an answer, one based on games of strategy such as chess and checkers: the chooser considers the choices that others will make and makes a choice that will lead to a better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily modified) is bad at predicting behavior. But instead of abandoning classical game theory, those in the social sciences have mounted a rescue operation under the name of “behavioral game theory.” Its main tool is to propose systematic deviations from the predictions of game theory, deviations that arise from character type, for example. Other deviations purportedly come from cognitive overload or limitations. The fundamental idea of behavioral game theory is that, if we know the deviations, then we can correct our predictions accordingly, and so get it right. There are two problems with this rescue operation, each of them is fatal. (i) For a chooser, contemplating the range of possible deviations, as there are many dozens, actually makes it exponentially harder to figure out a path to an outcome. This makes the theoretical models useless for modeling human thought or human behavior in general. (ii) Modeling deviations are helpful only if the deviations are consistent, so that scientists (and indeed decision makers) can make predictions about future choices on the basis of past choices. But the deviations are not consistent. In general, deviations from classical models are not consistent for any individual from one task to the next or between individuals for the same task. In addition, people's beliefs are in general not consistent with their choices. Accordingly, all hope is hollow that we can construct a general behavioral game theory. What can replace it? We survey some of the emerging candidates.

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Identifier

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extracted text

Against Game Theory
GALE M. LUCAS, MATHEW D. MCCUBBINS, and MARK TURNER

Abstract
People make choices. Often, the outcome depends on choices other people make.
What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers
an answer, one based on games of strategy such as chess and checkers: the chooser
considers the choices that others will make and makes a choice that will lead to a
better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily
modified) is bad at predicting behavior. But instead of abandoning classical game
theory, those in the social sciences have mounted a rescue operation under the name
of “behavioral game theory.” Its main tool is to propose systematic deviations from
the predictions of game theory, deviations that arise from character type, for example.
Other deviations purportedly come from cognitive overload or limitations. The fundamental idea of behavioral game theory is that, if we know the deviations, then we
can correct our predictions accordingly, and so get it right. There are two problems
with this rescue operation, each of them is fatal. (i) For a chooser, contemplating the
range of possible deviations, as there are many dozens, actually makes it exponentially harder to figure out a path to an outcome. This makes the theoretical models
useless for modeling human thought or human behavior in general. (ii) Modeling
deviations are helpful only if the deviations are consistent, so that scientists (and
indeed decision makers) can make predictions about future choices on the basis of
past choices. But the deviations are not consistent. In general, deviations from classical models are not consistent for any individual from one task to the next or between
individuals for the same task. In addition, people’s beliefs are in general not consistent with their choices. Accordingly, all hope is hollow that we can construct a general behavioral game theory. What can replace it? We survey some of the emerging
candidates.

INTRODUCTION
Scholars employ game theory to model interdependent decision-making in
bargaining, constitutional law, democratic stability, standard setting, gender
roles, social movements, communication, markets, voting, coalition formation, resource allocation, war, and many other domains. For a review, with
citations, see Lucas, McCubbins, and Turner (2013).
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

Game theory has been widely discredited: many studies have demonstrated game theory’s mispredictions. People seem to be highly sensitive
to frame or context and biased in their strategies. They follow heuristic
decision-making. They are limited in their ability to reason and learn. Many
attempts have been made to create a behavioral game theory by adding a
correction for each of four-dozen odd mispredictions (see Lucas et al., 2013).
But the span of mispredictions is so great and so varied that building in
corrections for them produces a model that is computationally intractable
for actual human beings.
REVIEW: THE ELEMENTS OF GAME THEORY
What is a game? A game, theoretically, is defined by identifying the players,
the actions available to them, the information they have about the game,
when they have such information, what they know about what others
know or will know and when those others will know it, the strategies
available to them that define rules for what actions they will take in making
decisions, the payoffs that come with outcomes, the range of outcomes,
and “equilibria.” The acronym for these dimensions is PAISPOE: players,
actions, information, strategies, payoffs, outcomes, and equilibria. What is
an equilibrium? An equilibrium is a path of choices made by players in the
game—a path that could happen, given the dispositions of all the players
as defined in game theory. An equilibrium concept is a rule a player uses to
pursue an equilibrium path. There are a number of proposed equilibrium
concepts that players might use. They have names such as “dominant
strategy,” “Nash equilibrium,” “Bayesian strategy,” “correlated strategy,”
and “subgame perfect Nash equilibrium (SPNE).” The classic game theory
equilibrium concepts are “dominant strategy” and “Nash equilibrium.”
A pure-strategy Nash equilibrium concept, for example, is a combination
of actions for all the players according to which no player can benefit by
unilaterally deviating from his or her combination. For a review of types
of equilibrium concepts, see Maschler, Solan, and Zamir (2013). To be
generalizable, all of the attempts to model interdependent choice, classical
or behavioral, must assume that (i) people follow equilibrium strategies,
(ii) there are specific types of people who choose a generalizable strategy
over a class of tasks, or (iii) all people in performing a specific task choose
a generalizable behavioral strategy. Behavioral game theory is trying to
build a layer cake on top of game theory, by adding layers to the original
model. Each additional layer consists of a correction to the foundation. For
example, prospect theory would eliminate certain strategies associated with
disfavored bets.

Against Game Theory

3

But the number of adjustments needed to build a behavioral game theory
is so vast that it cannot yield generalizable models. The literature has proposed many adjustments in terms of bounds, biases, heuristics, and context
dependencies. This presents two problems for behavioral game theory. First,
experimental economists working in the laboratory and knowing that subjects make one or more of these adjustments are no longer in the position of
knowing subjects’ true payoffs: we know only the experimental economists’
view of the experimental earnings, typically thought to be the subjects’ earnings. What experimentalists do not consider is “context,” that is, factors such
as unobserved experimenter demand and framing. Second, and most important, under such adjustments, we do not know what the subjects believe.
Most games, especially those simple enough to be tested in the lab and simple enough that we can strip out most (if not all) of the effect of framing
and context, assume that subjects share common knowledge. Classical game
theory requires players to have correct and consistent beliefs. To have “correct beliefs” is to regard other players as following classical game theory and
to predict that they follow classical equilibrium strategies. Indeed, it is also
required that players know that other players know that they themselves
are following classical strategies and so on, ad infinitum. As Lupia, Levine,
and Zharinova (2010) note, the condition is even stronger, in that a classical
equilibrium concept “requires shared conjectures … . Common Nash refinements … continue to require that actors share identical conjectures of other
players’ strategies” (p. 106). This is part of what economists assume when
they accept that the players in a game share “common knowledge.” As Smith
(2000, p. 9) writes, citing two other winners of the Bank of Sweden Prize in
Economic Sciences in Memory of Alfred Nobel:
“The common knowledge assumption underlies all of game theory and much
of economic theory. Whatever be the model under discussion … the model
itself must be assumed common knowledge; otherwise the model is insufficiently specified and the analysis incoherent” (Aumann 1987, p. 473). Without
such common knowledge people would fail to reason their way to the solution
arrived at cognitively by the theorist. This is echoed by Arrow (1987) when he
notes that a “monopolist, even … where there is just one in the entire economy,
has to understand all these [general equilibrium] repercussions … has to have
a full general equilibrium model of the economy.” (p. 207)1

Nash showed that any two-player zero-sum game has an equilibrium and
it was later proved that finding this equilibrium is computationally tractable.
(A zero-sum game has fixed payoffs, where higher payoffs to one player
result in corresponding lower payments to other players). This was the
1. Smith here quotes a reprint of an original article by Arrow (1986).

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

appeal of noncooperative game theory: we could find equilibria that in turn
predict outcomes of interest. But, even in the case where there are only two
players and two actions, we cannot expect humans to solve non-zero-sum
games, as they are computationally intractable or infeasible, falling into the
class of computational problems identified as PPAD-complete2 (for history,
definition, and analysis, see Daskalakis, Goldberg, & Papadimitriou, 2009;
see also Daskalakis, Goldberg, & Papadimitriou, 2005; Chen & Deng, 2006).
The core problem for building a behavioral game theory is that, as we
add the biases, heuristics, and context dependencies suggested by decades
of research, we are implicitly increasing the dimensionality of the computational problem of finding an equilibrium. It may seem that building a
range of possible deviations into the model would help us build a better
model. Doing so requires the bold assumption that a given subject, when
faced, for example, with a series of non-zero sum games, deviates from
classical game theory in a way that is consistent from one game to the next,
and even from one choice to the next inside the same game. The result is
indeed a generalizable theory—perhaps a false theory, but one that is at
least generalizable. But for that theory to give us purchase on modeling
human thought or predicting human behavior, the deviations in beliefs and
therefore strategies, must—at a minimum—be consistent. They also must
be common knowledge: subjects will have no way to compute consistent
strategies if the way in which subjects deviate from strategies is private
information belonging to only the capricious subject and unknowable to
other subjects. That is the bedrock on which the rescue operation for failed
game theory must be built. Our evidence, however, like all other evidence
of which we are aware that touches on this point, shows that this presumed
bedrock does not in fact exist.
NEW FINDINGS
RESEARCH DESIGN
There are two important new features of our experimental design. First,
we created a battery of tasks. Our experiments use a battery of up to 17
2. PPAD stands for “polynomial parity argument on directed graphs.” It is a complexity class regarded
as exceptionally difficult. In computational complexity theory, a problem X is called hard for a complexity
class C if any problem in C can be reduced to X, which implies that no problem in C is harder than X, as
a solution to X provides a solution to any problem in C. If X is both hard for C and in C, then X is called
C-complete. A problem that is C-complete is the hardest problem, computationally, in C, or rather, there
is no harder problem in C. A PPAD-complete problem is in principle “so hard to calculate that all the
computers in the world couldn’t find it in the lifetime of the universe” (Hardesty, 2009). Accordingly, it
is difficult to imagine that human beings playing a game would seek solutions by trying to perform such
a computation. “By showing that some common game-theoretical problems are so hard that they’d take
the lifetime of the universe to solve, Daskalakis is suggesting that they can’t accurately represent what
happens in the real world” (Hardesty, 2009).

Against Game Theory

5

games, several of which we constructed by modifying the standard form of
well-known games such as “Prisoner’s Dilemma,” “Public Goods,” “Stag
Hunt,” “Ultimatum,” “Trust,” “Chicken,” and “Dictator.” The purpose of
our modifications is to minimize or eliminate the framing of the game and
to present the games, to the extent possible, as starkly as they are defined
in prominent textbooks in game theory. For details, see Lucas et al. (2013).
We emphasize that, unlike the typical method of running experiments in
psychology and economics, where subjects face the same task repeatedly,
our method presents subjects with a battery of tasks. In addition, unlike
psychology experiments, where subjects are typically paid in the form of
satisfying a course requirement, and unlike economics experiments, where
subjects are typically paid at random for only one of the two to three dozen
repetitions of the task, our subjects know that they are paid in cash according
to every action they take in every task.
Second, we added prediction markets, based on Plott and Roust (2005) and
Wolfers and Zitzewitz (2004). In these prediction markets, subjects could earn
additional money by placing bets on the choices that were made by the players with whom they were matched and in many cases by placing bets on
the collective choices of all subjects who had played the game during previous runs of the experiment. We create a market, specifically a betting market,
where we invite subjects to bet on other players’ choices. We quiz the subjects on the betting procedure so that we could both motivate them to work
hard to understand what the bets entailed and also to measure each subject’s
compliance with respect to the betting tasks. The subjects were paid if their
bets regarding the other player’s actions were accurate and they were given
a chance to also double down on their bets if they felt confident about their
predictions. Subjects understood that they can earn this extra money from
betting, and how much for each bet. For example, in the Trust Game, there
are two players randomly paired—Player 1 and Player 2; both start with $5;
Player 1 can select any number of dollars from 0 to 5 to give away; those
dollars are taken from Player 1, tripled by the experimenters, and given to
Player 2; after receiving them, Player 2 has the opportunity to transfer back
any number of the dollars that Player 2 has in total, including Player 2’s original $5. At this point, Player 2 may have any number of dollars between 5
and 20. We ask Player 1 to guess how many dollars Player 2 will return.
Later, but before Player 2 learns Player 1’s choice, we ask Player 2 to guess
how many dollars Player 1 selected to give away. We also ask Player 2 to
guess how much Player 1 predicted Player 2 would transfer back to Player
1. After Player 2 learns Player 1’s choice, we then ask Player 2 to guess how
much Player 1 predicted that Player 2 would return. All players know that a
player earns $3 for each correct guess and nothing for a guess that is wrong.
The questions we ask vary slightly for each task, but, as an example, here

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

is an exact question we ask Player 1 in the Trust Game: “How much money
do you guess the other person transferred back to you? If you guess correctly, you will earn $3. If not, you will neither earn nor lose money.” Players
know that, with one exception, they can never learn whether their predictions
(bets) were right or wrong and that subjects never have any information about
other subjects’ guesses (bets). The exception is the rare case in which Player
2 in a sequential game, such as Trust or Ultimatum, must know Player 1’s
choice in order for Player 2 to understand Player 2’s situation and payoffs.
For example, Player 2 in Trust must be informed of how many dollars Player
1 chose to give away, if Player 2 is going to know how many dollars Player
2 has and therefore what the possible actions and payoffs are. Even then, the
delivery of this information to Player 2 and Player 2’s subsequent choice are
postponed to the last set of choices a Player makes, so as to have no effect
on previous choices. Payments to subjects are made in a lump sum, without
accounting or explanation, individually, anonymously, and privately, when
the experiment is completed.3 We do this to eliminate any opportunity for
subjects to make inferences about other players’ choices (either individually
or collectively), and subjects know this before they make any of their many
choices in the extensive battery. For details on these prediction markets in a
range of games, see Lucas et al. (2013).
RESULTS
Across our battery of tasks, our results verify decades of research demonstrating that subjects do not follow game-theoretic predictions. Consider a
traditional Ultimatum Game. According to Andreoni and Blanchard (2006,
p. 307), this game “has come to symbolize the power” of classical game theory and “its utter failure in practice.” In this “bargaining game,” a “proposer”
makes a take-it-or-leave-it offer to a “responder,” who then accepts or rejects
the offer. The classical equilibrium prediction is that if players care only about
their own monetary payoffs, then the responder will accept any positive offer
the “proposer” makes. (More technically, not counting the “endowment” of
dollars with which players begin—in our experiment, for example, the proposer begins with $10 and the responder with $0—if we assume that players
care only about the money they earn, then the Nash Equilibrium prediction
for the responder is that the responder will accept any positive offer the “proposer” makes; and the Nash equilibrium prediction for the proposer is that,
knowing that the responder will accept any positive offer, the proposer will
reason by backward induction to choose the smallest possible positive offer
allowed by the game.) Despite the stark framing of our experimental tasks,
3. Except for on time show up fees that were paid to all subjects and except for payments for the first
quiz relating to general experimental instructions.

Against Game Theory

7

our results generally replicate what others have found about the poverty of
classical Nash equilibrium predictions (see Camerer, 2003). For example, only
slightly more than 6% of our subjects chose the classical strategy when they
play the Ultimatum Game.
But the question we focus on with our battery of experimental games is,
when players “deviate” from the classical strategies, do they do so consistently? The answer is no, and if there is no consistency, then the modifications
to classical game theory cannot provide a generalizable model of behavior.
For example, the first half of our Trust Game is exactly like a game that we
call “Donation”: a given subject as Player 1 in Trust is in exactly the same
payoff and action situation as he or she is when he or she is the Donor in
Donation. Accordingly, we can measure whether a given subject is consistent
across these two situations. In addition, the second half of our Trust Game is
exactly like our Dictator Game: a given subject as Player 2 in our Trust Game
faces the same incentives and action possibilities as he or she faces when he
or she is the Dictator in our Dictator Game.4 We thus can measure whether a
given subject is consistent across these two situations. In addition, all subjects
completed a Trust Game where they made choices as Player 1 and also completed a Trust Game where they made choices as Player 2. We therefore can
examine the consistency of a given subject’s behavior within a game, namely
Trust (see Lucas et al., 2013, for details).
Our findings show that in Trust, there is large variance in behavior across
subjects in the role of Player 1 and also in the role of Player 2. (We discuss
findings in more detail in the Appendix.)
They also show that there is large variance in behavior by the same subject
in those two roles. We expected to find that subjects deviate from predicted
behavior for each and every task, but, for example, our results show much
more than that for Trust, Dictator, and Donation: fewer than 15% of our subjects deviate consistently from classical equilibrium concepts across the four
tasks involved in those games.5 For these four tasks, by even the most minimal definition of consistency, only 42% of our subjects either consistently
follow classical equilibrium concepts or consistently deviate from them. That
is, a minority of subjects have even the most minimal consistency from task
to task. We report on similar results in Lucas et al. (2013).
This suggests that simple amendments to game theory, such as adding
social preferences of one sort or another, risk preference, or discovering each
subject’s individual level of experience or ability to undertake the reasoning
necessary to choose an optimal strategy, or the level of randomness in each
4. Of course, one difference remains, the Trust task is interactive, whereas the Dictator task is not.
5. That is, in making choices as Player 1 or Player 2 in Trust, in making choices in Dictator or Ultimatum, subjects sometimes deviate and sometimes do not deviate from classical Nash equilibrium predictions. Those that deviate do not always do so, and few subjects deviate on every choice and few never
deviate.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

individual’s choices, cannot by themselves explain the inconsistent pattern
of choices across the battery of games in our experiment. For example,
sometimes the subject may “appear” altruistic, in one choice, and then
“appear” greedy in another choice, even though the incentives are identical
and are stated identically for the two tasks. Some subjects are altruistic some
of the time, other subjects are altruistic most of the time, and some subjects
are never altruistic. At best, we need amendments to game theory that
differ for each and every game and for each individual. This would make it
difficult, or impossible, to provide a general explanation of behavior that is
built on game theory.
Game theoretic predictions about behavior depend on the assumption
that beliefs and choices are aligned. Researchers rarely possess knowledge
of the actual beliefs of subjects. But our within-subject experiments allow
us to test beliefs, and we find that for individual subjects, there is routine
and ubiquitous inconsistency across choice and beliefs (see Appendix and
McCubbins, Turner, & Weller, 2012). We demonstrate that subjects’ beliefs
are often inconsistent with equilibrium predictions, which has not been
widely appreciated. Our findings also show that these deviations are not
consistent; they depend on the specific setting and task. These deviations
are so pervasive and so various even within a single subject that is seems
unwarranted to refer to them as deviations. On the contrary, consistent “Nash
behavior and beliefs” appear to be remarkable deviations from human
cognitive patterns and human behavior.
ADVANCE DIRECTIVE FOR BEHAVIORAL GAME THEORY:
DO NOT RESUSCITATE
Our results show, as has often been shown, that subjects deviate from the predictions made by classical equilibrium analysis in game theory. We emphasize that (i) subjects often deviate from these predictions, but that (ii) for
the vast majority of subjects, their deviations are themselves not consistent
even across similar tasks, and (iii) there is large variance in how different
subjects choose for any individual task. Moreover, we show (iv) that individuals’ beliefs about other subject’s choices or beliefs do not support classical
Nash equilibrium strategies, and (v) that there is large variance between subjects and among a single subject’s beliefs from task to task. In addition, we
show that individuals do not hold common beliefs about game strategy or
deviations from equilibrium. Individuals’ beliefs seem to be specific to particular settings and not generalizable from one setting to the next. Indeed,
it may be misleading to refer to these patterns of action and belief as “deviations” at all. There are no consistent deviations from classical equilibrium
concepts, and thus there is no general behavioral fix. There are about four

Against Game Theory

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dozen deviations from classical game theoretic predictions identified in the
literature. We find that the same individual subject will be deviating from
game theoretic predictions in as many ways as there are tasks in our experiment and that across all subjects in our experiment we see a great variability
from one subject to the next in the pattern of deviations. It is unsurprising, for
example, that some subjects are altruistic in some settings. It is unsurprising
that we find that some fraction of the subjects are altruistic for one or another
task. It is more surprising that subjects are altruistic in one task and then
not altruistic when offered the identical incentives again later on. All these
different variations of course interact with each other, giving a complex and
unpredictable landscape of complex variation running over individuals and
groups. Thus, adding behavioral assumptions to the general model of cognition within game theory cannot make these general models more suitable
for predicting behavior.
We have shown further that the protected core of game theory—the
unrecognized cognitive model, or Theory of Mind (McCubbins et al., 2012),
of noncooperative game theory—fails repeatedly in hypothesis testing. The
assumptions about human cognition that are part of game theory, including
the predictions of classical game theory and its refinements, are at odds with
what we know about actual human cognition. This is no surprise, because
the equilibrium concepts were not constructed based on how actual humans
think, reason, or make decisions. We do not yet see a way forward to creating
a behavioral game theory that offers meaningfully generalizable predictions.
Accordingly, our advance directive would say: Do Not Resuscitate.
THE NEXT STEP
What are the alternatives to game theory, both classical and behavioral? What
possibilities are there for forming testable hypotheses about interdependent
decision-making?6 Within cognitive science, there are a number of lines of
research about how actual human beings make actual decisions, several of
them reviewed by Turner (2001). These lines of research in cognitive science
have had virtually no consideration inside economics. Here are a few of them:
Variation Across Domains and Situations. Entire subfields of cognitive science
are dedicated to the ways in which human thought varies across different
domains and situations. Given basic considerations of evolutionary development and fitness, there is no reason to assume a priori that the way a human
6. Another way in which behavioral game theory has sought to account for ubiquitous deviations
from game-theoretic predictions is to add a random factor to human decision-making. One such prominent approach is “quantal response equilibrium” (see McKelvey & Palfrey, 1995). But it is largely impossible to put quantal response equilibrium to the test as almost any pattern of behavior is consistent with its
predictions (see McCubbins et al., 2013), especially when it is expanded to “heterogenous quantal response
equilibrium” (Rogers, Palfrey, & Camerer, 2009).

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

being thinks and acts with respect to food, mating, entertainment, and so
on would follow the same patterns or principles of reasoning and decision.
All models of game theory, classical and behavioral, assume the opposite,
namely, that although people might have different preferences with respect
to these different domains, their patterns of reasoning and choice must be
uniform across them. Game theory models two situations as identical if they
have the same game structure, regardless of the content. It does not matter,
for example, that the “Stag Hunt” game might concern growing vegetables or
killing soldiers. To a cognitive scientist, or maybe just to anybody other than
a game theorist, that approach looks like a nonstarter. It certainly should be
discarded as an assumption.
Learning. Entire subfields of cognitive science are dedicated to the various mental operations involved in learning, and to the study of how human
thought and action depend on the highly flexible and powerful learning for
which human beings are equipped. To give one example, cognitive science
routinely considers the power of analogy or blending: one remembers a previous specific situation, perhaps in childhood, or from a biography, or even
from a science fiction novel, and remembers, too, its outcomes; one then uses
those concepts and knowledge to inform one’s understanding and decisions
in the present specific situation. These traditions in cognitive science have
no status inside game theory, even though they provide a basis for hypotheses and tests about decision-making. Indeed, the validity of measuring such
powers of analogy and blending is so unquestioned in Western culture that
assessments of this ability are used as part of the process of deciding who has
what IQ and which applicants to college should be admitted.
Complexity and Nonlinearity. The world is rich, and in the typical situation,
actors are engaged in simultaneous games that overlap. In life, any action
is usually a move in many different games. Strategies to maximize expected
utility over all these games are typically nonlinear. In principle, the output of
any subgame of any game can be input to any subgame of any other game.
Game theory by contrast assumes a partitioning of thought and action to tiny
scripts of activity that are pretty much separate from all others. This assumption could be discarded.
Adaptive Behavior. In the typical situation, people are adaptive: their first and
strongest disposition is often not to play the game but to reinvent it, change
it. Their decisions can be driven by attempts to change the game from the
outside. Game theory leaves no room for this normal and routine thought
and behavior.
Construal. Cognitive science routinely investigates our rich capacities for
differing construals of the same given material. “The mountain range runs
from Canada to Mexico” and “The mountain range runs from Mexico to
Canada” deal with the same stuff but call for quite different emphases

Against Game Theory

11

and viewpoints. They also both call for conceptualization by using the
idea of motion (“runs from … to”), even though in some sense we think
that no motion is involved. Construal is a crucial part of interdependent
decision-making, because actors try to reconstrue history and to get other
actors to do the same. In the typical situation, actors work at conceptual
reinterpretation of the history of play, so as to persuade other actors that the
value and status of a past action must be changed, and further, to persuade
them that the action led to nodes different from those to which it was once
thought to lead. Conceptually, the history of the game is not fixed. Game
theory assumes the opposite.
What’s Up? Actors must operate in general without knowing what game
they are in, and the question always arises, who has the authority to recognize and establish the game being played? Actors attempt to influence other
actors’ thoughts about the game being played.
Identity. Cognitive science routinely considers the work people do to
construct an identity for themselves, and to carry it and vary it appropriately
from situation to situation. It may often be that the principle payoff in any
scripted activity is not the local payoffs but the actor’s concept of a personal
identity. When we enter different situations, different rooms, different
moments, what does the present offer by way of allowing us to construct an
identity? What looks like fatal inconsistency from the point of view of game
theory might look like fruitful experimentation, learning, and fluidity from
the point of view of actual human beings.
Within the social sciences, it has been shown that institutions (laws,
constitutions, auction mechanisms, common agency, families, friendships,
societal structures, and so on) serve to create not only incentives for choice
but also a set of shared mental models about players, actions, payoffs,
outcomes, and perhaps most important, information. This would imply that
the study of institutions might supply some of the cognitive grounding that
game theory is currently lacking. Yet another assumption of game theory
is that from knowledge about players, actions, payoffs, outcomes, and
information, one can derive strategies and equilibria. It is unknown whether
this is true, but what is clear is that institutions have already influenced
how subjects derive strategies and equilibria. People, developed within
institutions, are thus, when they enter our experiments, far from a tabula
rasa. There is little reason to imagine that the narratives that we can give
them in an experiment are strong enough to offer much hope of overcoming
that training within institutions. There is little reason to think that these
narratives in experiments would substitute for the purported “10,000 h” of
learning and practice needed to be successful at a given task. Accordingly,
the cognitive study of decision-making must include the study of learning
within institutions.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

In short, we think that the future for game theory, if there is one, would
come from a grounding in cognitive science, or more generally, in the analysis of how the cognitively modern human mind works, what its basic mental
operations are, and how they are deployed in situations. We know that strategic games such as chess arose very late in human evolution and even in
human culture and that people are very poor at such games in general and
must undergo extensive training in order to play them well. Such games of
strategy are perhaps the last place one should look for a model of human
decision-making generally. Game theory has placed itself into that cul-de-sac,
but there is no reason for that sterility and isolation. One could instead begin
with how actual human beings think.
APPENDIX ON EXPERIMENTAL DATA
This appendix provides details of subjects’ behavior in Trust, Dictator, and
Donation. First, on examining the play within the Trust Game, we find that
56% of the subjects as Player 1 sent money to Player 2. On average, they
sent $1.43, with a standard deviation of $1.70. On average, as Player 2, they
return $1.23, with a standard deviation of $2.29. Our emphasis is not on the
well-established deviance from classical predictions in Trust (indeed, the
standard deviation from our experiments is somewhat smaller than that
usually reported) but rather on the large variance in behavior both across
subjects in both tasks and by the same subject across different tasks. Only
1 of the 80 subjects who as Player 2 received $0 from Player 1 returned any
money to Player 1. Of the 100 subjects who did receive money as Player
2, 62 returned something. The average returned for this subset is $2.22,
again with a large variance (the standard deviation is $2.71). Second, for
the 62 who as Player 2 returned money to Player 1 after receiving money,
only 40 sent money when they were the Dictator; and of those 40, only 29
sent money when they were in the role of Donor. Was a subject’s pattern
of deviation from classical equilibrium consistent? There are 42 subjects
who deviate from classical equilibrium as both Player 1 and Player 2 in
Trust. Of these 42, 33 also deviated as Donor and, of these 33, 26 deviated
as Dictator. We see that fewer than 15% of our subjects consistently deviate
from classical equilibrium concepts across these four tasks. In sum, by even
the most minimal definition of consistency, only 42% of our subjects either
consistently follow classical equilibrium concepts (specifically, “SPNE”)
or consistently deviate from them, in these four tasks. That is, a minority
of subjects have even the most minimal consistency from task to task. We
report on similar results in the study by Lucas et al. (2013).
We turn now to reporting on the often hidden and never-tested parts of
“equilibrium concepts” in game theory, that is, the assumptions regarding

Against Game Theory

13

subjects’ beliefs and knowledge. In the Trust Game, for example, the classical
SPNE prediction for both players is that they will send $0 for all tasks. Thus,
if our subjects hold beliefs that support SPNE, both Player 1 and Player 2
should expect the other person in each task to send $0. Further, they should
expect that the other player expects that they will send $0. (And so on ad
infinitum, they should expect that the other expects that they expect that the
other player will send $0, and so on.) When acting as Trust Player 1, however,
88 of 180 subjects bet, and thus can be thought to believe, that Player 2 will
return some money to them. Likewise, when in the role of Player 2 in Trust,
the majority of participants (112 of 180) believe that Player 1 will send them
more than the equilibrium amount of $0. Indeed, only 21% (38 of 180) hold the
“correct” SPNE beliefs and, as both Player 1 and Player 2, bet that the other
person will send nothing. (More elaborately, as the “other person” is always
that other subject with whom the subject has been randomly paired for that
specific task, only 21% of the players expect both when they are Player 1 and
later when they are Player 2 that the other subject with whom they have been
randomly paired for that particular game will send nothing.) In total, 58 of
180 participants bet when they are in both roles—that is, Player 1 and Player
2—that the other person will send more than $0. In general, participants do
not hold beliefs that support a SPNE.
Examining consistency of belief in more depth, we can ask, for example,
how many of the 180 subjects in our analysis consistently held beliefs that
support an SPNE? As Player 2, participants made guesses about Player 1’s
prediction of how much Player 2 would return, and only 92 of 180 made
guesses that support an SPNE. Of those 92, only 41 also held SPNE-consistent
beliefs as Player 2 when guessing how much Player 1 predicted that Player 2
guessed Player 1 would transfer. Of those 41, 33 were also SPNE-consistent
as Player 2 when guessing how much Player 1 would transfer. Of those 33,
29 were also SPNE-consistent as Player 1 when guessing how much Player
2 predicted that Player 1 guessed that Player 2 would return. Of those 29,
27 were also SPNE-consistent as Player 1 when guessing both (i) how much
Player 2 would return and (ii) how much Player 2 predicted that Player 1
would send. In sum, only 15% of our subjects consistently adhere to beliefs
that support an SPNE as Player 1 and as Player 2 in a single game, Trust.
REFERENCES
Andreoni, J., & Blanchard, E. (2006). Testing subgame perfection apart from fairness
in ultimatum games. Experimental Economics, 9, 307–321.
Arrow, K. J. (1986). Rationality of self and others in an economic system. The Journal of Business, 59(4), Part 2: The Behavioral Foundations of Economic Theory. pp.
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Aumann, R. (1987). Game theory. In New palgrave dictionary of economics (Vol. 2, p.
473). New York, NY: Macmillan.
Camerer, C. F. (2003). Behavioral game theory: Experiments in strategic interaction.
Princeton, NJ: Princeton University Press.
Chen, X., and Deng, X. (2006). Settling the complexity of 2-player Nash-equilibrium.
Proceedings of the 47th Annual IEEE symposium on foundations of computer science
(FOCS’06; pp. 261–272). doi:10.1109/FOCS.2006.69
Daskalakis, C., Goldberg, P. W., & Papadimitriou, C. H. (2005). The complexity
of computing a Nash equilibrium (TR05–115). Electronic Colloquium on Computational Complexity. Retrieved from http://eccc.hpi-web.de/eccc-reports/
2005/TR05-115
Daskalakis, C., Goldberg, P. W., & Papadimitriou, C. H. (2009). The complexity
of computing a Nash equilibrium. Communications of the ACM, 52(2), 89–97.
doi:10.1145/1461928.1461951
Hardesty, L. (2009, November 9). What computer science can teach economics. MIT
News. Retrieved from http://web.mit.edu/newsoffice/2009/game-theory.html
Lucas, G., McCubbins, M., & Turner, M. (2013). Can we build behavioral
game theory? Available at SSRN: http://ssrn.com/abstract=2278029 or 10.2139/
ssrn.2278029
Lupia, A., Levine, A. S., & Zharinova, N. (2010). Should political scientists use the
self confirming equilibrium concept? Benefits, costs and an application to the Jury
Theorem. Political Analysis, 18, 103–123.
Maschler, M., Solan, E., & Zamir, S. (2013). Game theory. Cambridge, England: Cambridge University Press.
McCubbins, M. D., Turner, M., & Weller, N. (2012). The theory of minds within the
theory of games. In H. R. Arabnia, D. de la Fuente, E. G. Kozerenko, P. M. LaMonica, R. A. Liuzzi, J. A. Olivas, A. M. G. Solo & T. Waskiewica (Eds.), Proceedings
of the 2012 international conference on artificial intelligence (Vol. I, pp. 515–521). Las
Vegas, NV: CSREA Press.
McCubbins, M. D., Turner, M., & Weller, N. (2013). Testing the foundations of quantal
response equilibrium. In A. M. Greenberg, W. G. Kennedy & N. D. Bos (Eds.),
Social computing, behavioral-cultural modeling and prediction. Lecture notes in computer
science (Vol. 7812, pp. 144–153). Berlin: Springer.
McKelvey, R., & Palfrey, T. (1995). Quantial response equilibria for normal form
games. Games and Economic Behavior, 10, 6–38.
Plott, C. & Roust, K. (2005). The design and testing of information aggregation mechanisms: a two-stage parimutuel IAM. Social Science Working Paper #
1245. Pasadena, California Institute of Technology. Retrieved from http://www.
hss.caltech.edu/SSPapers/sswp1245.pdf
Rogers, B. W., Palfrey, T. R., & Camerer, C. F. (2009). Heterogeneous quantal response
equilibrium and cognitie hierarchies. Journal of Economic Theory, 144(4), 1440–1467.
Smith, V. (2000). “Rational choice: The contrast between economics and psychology”
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Turner, M. (2001). “Choice,” chapter 3 of Cognitive dimensions of social science. New
York, NY: Oxford University Press.
Wolfers, J., & Zitzewitz, E. (2004). Prediction markets. Journal of Economic Perspectives.

GALE M. LUCAS SHORT BIOGRAPHY
Gale M. Lucas is currently a postdoctoral research associate at University of
Southern California’s Institute for Creative Technologies. She is also affiliated
with USC’s Marshall School of Business. Dr. Lucas earned her PhD in Social
Psychology from Northwestern University, where she was named a National
Science Foundation Graduate Research Fellow. She has taught at Northwestern University, Willamette University, and Western Oregon University.
MATHEW D. MCCUBBINS SHORT BIOGRAPHY
Mathew D. McCubbins is Professor of Political Science and Law at Duke
University, and Director of the Center for Democracy and the Rule of Law,
Duke School of Law. Web page with link to CV: www.mccubbins.us
MARK TURNER SHORT BIOGRAPHY
Mark Turner is Institute Professor and Professor of Cognitive Science at Case
Western Reserve University. He is the Founding Director of the Cognitive
Science Network; Co-Director of the Red Hen Lab; Founding President of
the Myrifield Institute for Cognition and the Arts; Fellow of the Institute
for Advanced Study, the Center for Advanced Study in the Behavioral
Sciences, the National Humanities Center, the John Simon Guggenheim
Memorial Foundation, the Institute of Advanced Study at Durham University, the Centre for Advanced Study at the Norwegian Academy of
Science and Letters, the New England Institute for Cognitive Science and
Evolutionary Psychology, the National Endowment for the Humanities,
and the Institute for the Science of Origins; Extraordinary Member of the
Humanwissenschaftliches Zentrum der Ludwig-Maximilians-Universität;
and External Research Professor of the Krasnow Institute for Advanced
Study. His research is presented at http://markturner.org
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16

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

Agency as an Explanatory Key: Theoretical Issues (Sociology), Richard
Biernacki and Tad Skotnicki
Choice Architecture (Psychology), Adrian R. Camilleri and Rick P. Larrick
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Andrei Cimpian
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Kandler et al.
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and Dare A. Baldwin



Against Game Theory
GALE M. LUCAS, MATHEW D. MCCUBBINS, and MARK TURNER

Abstract
People make choices. Often, the outcome depends on choices other people make.
What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers
an answer, one based on games of strategy such as chess and checkers: the chooser
considers the choices that others will make and makes a choice that will lead to a
better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily
modified) is bad at predicting behavior. But instead of abandoning classical game
theory, those in the social sciences have mounted a rescue operation under the name
of “behavioral game theory.” Its main tool is to propose systematic deviations from
the predictions of game theory, deviations that arise from character type, for example.
Other deviations purportedly come from cognitive overload or limitations. The fundamental idea of behavioral game theory is that, if we know the deviations, then we
can correct our predictions accordingly, and so get it right. There are two problems
with this rescue operation, each of them is fatal. (i) For a chooser, contemplating the
range of possible deviations, as there are many dozens, actually makes it exponentially harder to figure out a path to an outcome. This makes the theoretical models
useless for modeling human thought or human behavior in general. (ii) Modeling
deviations are helpful only if the deviations are consistent, so that scientists (and
indeed decision makers) can make predictions about future choices on the basis of
past choices. But the deviations are not consistent. In general, deviations from classical models are not consistent for any individual from one task to the next or between
individuals for the same task. In addition, people’s beliefs are in general not consistent with their choices. Accordingly, all hope is hollow that we can construct a general behavioral game theory. What can replace it? We survey some of the emerging
candidates.

INTRODUCTION
Scholars employ game theory to model interdependent decision-making in
bargaining, constitutional law, democratic stability, standard setting, gender
roles, social movements, communication, markets, voting, coalition formation, resource allocation, war, and many other domains. For a review, with
citations, see Lucas, McCubbins, and Turner (2013).
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

1

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

Game theory has been widely discredited: many studies have demonstrated game theory’s mispredictions. People seem to be highly sensitive
to frame or context and biased in their strategies. They follow heuristic
decision-making. They are limited in their ability to reason and learn. Many
attempts have been made to create a behavioral game theory by adding a
correction for each of four-dozen odd mispredictions (see Lucas et al., 2013).
But the span of mispredictions is so great and so varied that building in
corrections for them produces a model that is computationally intractable
for actual human beings.
REVIEW: THE ELEMENTS OF GAME THEORY
What is a game? A game, theoretically, is defined by identifying the players,
the actions available to them, the information they have about the game,
when they have such information, what they know about what others
know or will know and when those others will know it, the strategies
available to them that define rules for what actions they will take in making
decisions, the payoffs that come with outcomes, the range of outcomes,
and “equilibria.” The acronym for these dimensions is PAISPOE: players,
actions, information, strategies, payoffs, outcomes, and equilibria. What is
an equilibrium? An equilibrium is a path of choices made by players in the
game—a path that could happen, given the dispositions of all the players
as defined in game theory. An equilibrium concept is a rule a player uses to
pursue an equilibrium path. There are a number of proposed equilibrium
concepts that players might use. They have names such as “dominant
strategy,” “Nash equilibrium,” “Bayesian strategy,” “correlated strategy,”
and “subgame perfect Nash equilibrium (SPNE).” The classic game theory
equilibrium concepts are “dominant strategy” and “Nash equilibrium.”
A pure-strategy Nash equilibrium concept, for example, is a combination
of actions for all the players according to which no player can benefit by
unilaterally deviating from his or her combination. For a review of types
of equilibrium concepts, see Maschler, Solan, and Zamir (2013). To be
generalizable, all of the attempts to model interdependent choice, classical
or behavioral, must assume that (i) people follow equilibrium strategies,
(ii) there are specific types of people who choose a generalizable strategy
over a class of tasks, or (iii) all people in performing a specific task choose
a generalizable behavioral strategy. Behavioral game theory is trying to
build a layer cake on top of game theory, by adding layers to the original
model. Each additional layer consists of a correction to the foundation. For
example, prospect theory would eliminate certain strategies associated with
disfavored bets.

Against Game Theory

3

But the number of adjustments needed to build a behavioral game theory
is so vast that it cannot yield generalizable models. The literature has proposed many adjustments in terms of bounds, biases, heuristics, and context
dependencies. This presents two problems for behavioral game theory. First,
experimental economists working in the laboratory and knowing that subjects make one or more of these adjustments are no longer in the position of
knowing subjects’ true payoffs: we know only the experimental economists’
view of the experimental earnings, typically thought to be the subjects’ earnings. What experimentalists do not consider is “context,” that is, factors such
as unobserved experimenter demand and framing. Second, and most important, under such adjustments, we do not know what the subjects believe.
Most games, especially those simple enough to be tested in the lab and simple enough that we can strip out most (if not all) of the effect of framing
and context, assume that subjects share common knowledge. Classical game
theory requires players to have correct and consistent beliefs. To have “correct beliefs” is to regard other players as following classical game theory and
to predict that they follow classical equilibrium strategies. Indeed, it is also
required that players know that other players know that they themselves
are following classical strategies and so on, ad infinitum. As Lupia, Levine,
and Zharinova (2010) note, the condition is even stronger, in that a classical
equilibrium concept “requires shared conjectures … . Common Nash refinements … continue to require that actors share identical conjectures of other
players’ strategies” (p. 106). This is part of what economists assume when
they accept that the players in a game share “common knowledge.” As Smith
(2000, p. 9) writes, citing two other winners of the Bank of Sweden Prize in
Economic Sciences in Memory of Alfred Nobel:
“The common knowledge assumption underlies all of game theory and much
of economic theory. Whatever be the model under discussion … the model
itself must be assumed common knowledge; otherwise the model is insufficiently specified and the analysis incoherent” (Aumann 1987, p. 473). Without
such common knowledge people would fail to reason their way to the solution
arrived at cognitively by the theorist. This is echoed by Arrow (1987) when he
notes that a “monopolist, even … where there is just one in the entire economy,
has to understand all these [general equilibrium] repercussions … has to have
a full general equilibrium model of the economy.” (p. 207)1

Nash showed that any two-player zero-sum game has an equilibrium and
it was later proved that finding this equilibrium is computationally tractable.
(A zero-sum game has fixed payoffs, where higher payoffs to one player
result in corresponding lower payments to other players). This was the
1. Smith here quotes a reprint of an original article by Arrow (1986).

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

appeal of noncooperative game theory: we could find equilibria that in turn
predict outcomes of interest. But, even in the case where there are only two
players and two actions, we cannot expect humans to solve non-zero-sum
games, as they are computationally intractable or infeasible, falling into the
class of computational problems identified as PPAD-complete2 (for history,
definition, and analysis, see Daskalakis, Goldberg, & Papadimitriou, 2009;
see also Daskalakis, Goldberg, & Papadimitriou, 2005; Chen & Deng, 2006).
The core problem for building a behavioral game theory is that, as we
add the biases, heuristics, and context dependencies suggested by decades
of research, we are implicitly increasing the dimensionality of the computational problem of finding an equilibrium. It may seem that building a
range of possible deviations into the model would help us build a better
model. Doing so requires the bold assumption that a given subject, when
faced, for example, with a series of non-zero sum games, deviates from
classical game theory in a way that is consistent from one game to the next,
and even from one choice to the next inside the same game. The result is
indeed a generalizable theory—perhaps a false theory, but one that is at
least generalizable. But for that theory to give us purchase on modeling
human thought or predicting human behavior, the deviations in beliefs and
therefore strategies, must—at a minimum—be consistent. They also must
be common knowledge: subjects will have no way to compute consistent
strategies if the way in which subjects deviate from strategies is private
information belonging to only the capricious subject and unknowable to
other subjects. That is the bedrock on which the rescue operation for failed
game theory must be built. Our evidence, however, like all other evidence
of which we are aware that touches on this point, shows that this presumed
bedrock does not in fact exist.
NEW FINDINGS
RESEARCH DESIGN
There are two important new features of our experimental design. First,
we created a battery of tasks. Our experiments use a battery of up to 17
2. PPAD stands for “polynomial parity argument on directed graphs.” It is a complexity class regarded
as exceptionally difficult. In computational complexity theory, a problem X is called hard for a complexity
class C if any problem in C can be reduced to X, which implies that no problem in C is harder than X, as
a solution to X provides a solution to any problem in C. If X is both hard for C and in C, then X is called
C-complete. A problem that is C-complete is the hardest problem, computationally, in C, or rather, there
is no harder problem in C. A PPAD-complete problem is in principle “so hard to calculate that all the
computers in the world couldn’t find it in the lifetime of the universe” (Hardesty, 2009). Accordingly, it
is difficult to imagine that human beings playing a game would seek solutions by trying to perform such
a computation. “By showing that some common game-theoretical problems are so hard that they’d take
the lifetime of the universe to solve, Daskalakis is suggesting that they can’t accurately represent what
happens in the real world” (Hardesty, 2009).

Against Game Theory

5

games, several of which we constructed by modifying the standard form of
well-known games such as “Prisoner’s Dilemma,” “Public Goods,” “Stag
Hunt,” “Ultimatum,” “Trust,” “Chicken,” and “Dictator.” The purpose of
our modifications is to minimize or eliminate the framing of the game and
to present the games, to the extent possible, as starkly as they are defined
in prominent textbooks in game theory. For details, see Lucas et al. (2013).
We emphasize that, unlike the typical method of running experiments in
psychology and economics, where subjects face the same task repeatedly,
our method presents subjects with a battery of tasks. In addition, unlike
psychology experiments, where subjects are typically paid in the form of
satisfying a course requirement, and unlike economics experiments, where
subjects are typically paid at random for only one of the two to three dozen
repetitions of the task, our subjects know that they are paid in cash according
to every action they take in every task.
Second, we added prediction markets, based on Plott and Roust (2005) and
Wolfers and Zitzewitz (2004). In these prediction markets, subjects could earn
additional money by placing bets on the choices that were made by the players with whom they were matched and in many cases by placing bets on
the collective choices of all subjects who had played the game during previous runs of the experiment. We create a market, specifically a betting market,
where we invite subjects to bet on other players’ choices. We quiz the subjects on the betting procedure so that we could both motivate them to work
hard to understand what the bets entailed and also to measure each subject’s
compliance with respect to the betting tasks. The subjects were paid if their
bets regarding the other player’s actions were accurate and they were given
a chance to also double down on their bets if they felt confident about their
predictions. Subjects understood that they can earn this extra money from
betting, and how much for each bet. For example, in the Trust Game, there
are two players randomly paired—Player 1 and Player 2; both start with $5;
Player 1 can select any number of dollars from 0 to 5 to give away; those
dollars are taken from Player 1, tripled by the experimenters, and given to
Player 2; after receiving them, Player 2 has the opportunity to transfer back
any number of the dollars that Player 2 has in total, including Player 2’s original $5. At this point, Player 2 may have any number of dollars between 5
and 20. We ask Player 1 to guess how many dollars Player 2 will return.
Later, but before Player 2 learns Player 1’s choice, we ask Player 2 to guess
how many dollars Player 1 selected to give away. We also ask Player 2 to
guess how much Player 1 predicted Player 2 would transfer back to Player
1. After Player 2 learns Player 1’s choice, we then ask Player 2 to guess how
much Player 1 predicted that Player 2 would return. All players know that a
player earns $3 for each correct guess and nothing for a guess that is wrong.
The questions we ask vary slightly for each task, but, as an example, here

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

is an exact question we ask Player 1 in the Trust Game: “How much money
do you guess the other person transferred back to you? If you guess correctly, you will earn $3. If not, you will neither earn nor lose money.” Players
know that, with one exception, they can never learn whether their predictions
(bets) were right or wrong and that subjects never have any information about
other subjects’ guesses (bets). The exception is the rare case in which Player
2 in a sequential game, such as Trust or Ultimatum, must know Player 1’s
choice in order for Player 2 to understand Player 2’s situation and payoffs.
For example, Player 2 in Trust must be informed of how many dollars Player
1 chose to give away, if Player 2 is going to know how many dollars Player
2 has and therefore what the possible actions and payoffs are. Even then, the
delivery of this information to Player 2 and Player 2’s subsequent choice are
postponed to the last set of choices a Player makes, so as to have no effect
on previous choices. Payments to subjects are made in a lump sum, without
accounting or explanation, individually, anonymously, and privately, when
the experiment is completed.3 We do this to eliminate any opportunity for
subjects to make inferences about other players’ choices (either individually
or collectively), and subjects know this before they make any of their many
choices in the extensive battery. For details on these prediction markets in a
range of games, see Lucas et al. (2013).
RESULTS
Across our battery of tasks, our results verify decades of research demonstrating that subjects do not follow game-theoretic predictions. Consider a
traditional Ultimatum Game. According to Andreoni and Blanchard (2006,
p. 307), this game “has come to symbolize the power” of classical game theory and “its utter failure in practice.” In this “bargaining game,” a “proposer”
makes a take-it-or-leave-it offer to a “responder,” who then accepts or rejects
the offer. The classical equilibrium prediction is that if players care only about
their own monetary payoffs, then the responder will accept any positive offer
the “proposer” makes. (More technically, not counting the “endowment” of
dollars with which players begin—in our experiment, for example, the proposer begins with $10 and the responder with $0—if we assume that players
care only about the money they earn, then the Nash Equilibrium prediction
for the responder is that the responder will accept any positive offer the “proposer” makes; and the Nash equilibrium prediction for the proposer is that,
knowing that the responder will accept any positive offer, the proposer will
reason by backward induction to choose the smallest possible positive offer
allowed by the game.) Despite the stark framing of our experimental tasks,
3. Except for on time show up fees that were paid to all subjects and except for payments for the first
quiz relating to general experimental instructions.

Against Game Theory

7

our results generally replicate what others have found about the poverty of
classical Nash equilibrium predictions (see Camerer, 2003). For example, only
slightly more than 6% of our subjects chose the classical strategy when they
play the Ultimatum Game.
But the question we focus on with our battery of experimental games is,
when players “deviate” from the classical strategies, do they do so consistently? The answer is no, and if there is no consistency, then the modifications
to classical game theory cannot provide a generalizable model of behavior.
For example, the first half of our Trust Game is exactly like a game that we
call “Donation”: a given subject as Player 1 in Trust is in exactly the same
payoff and action situation as he or she is when he or she is the Donor in
Donation. Accordingly, we can measure whether a given subject is consistent
across these two situations. In addition, the second half of our Trust Game is
exactly like our Dictator Game: a given subject as Player 2 in our Trust Game
faces the same incentives and action possibilities as he or she faces when he
or she is the Dictator in our Dictator Game.4 We thus can measure whether a
given subject is consistent across these two situations. In addition, all subjects
completed a Trust Game where they made choices as Player 1 and also completed a Trust Game where they made choices as Player 2. We therefore can
examine the consistency of a given subject’s behavior within a game, namely
Trust (see Lucas et al., 2013, for details).
Our findings show that in Trust, there is large variance in behavior across
subjects in the role of Player 1 and also in the role of Player 2. (We discuss
findings in more detail in the Appendix.)
They also show that there is large variance in behavior by the same subject
in those two roles. We expected to find that subjects deviate from predicted
behavior for each and every task, but, for example, our results show much
more than that for Trust, Dictator, and Donation: fewer than 15% of our subjects deviate consistently from classical equilibrium concepts across the four
tasks involved in those games.5 For these four tasks, by even the most minimal definition of consistency, only 42% of our subjects either consistently
follow classical equilibrium concepts or consistently deviate from them. That
is, a minority of subjects have even the most minimal consistency from task
to task. We report on similar results in Lucas et al. (2013).
This suggests that simple amendments to game theory, such as adding
social preferences of one sort or another, risk preference, or discovering each
subject’s individual level of experience or ability to undertake the reasoning
necessary to choose an optimal strategy, or the level of randomness in each
4. Of course, one difference remains, the Trust task is interactive, whereas the Dictator task is not.
5. That is, in making choices as Player 1 or Player 2 in Trust, in making choices in Dictator or Ultimatum, subjects sometimes deviate and sometimes do not deviate from classical Nash equilibrium predictions. Those that deviate do not always do so, and few subjects deviate on every choice and few never
deviate.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

individual’s choices, cannot by themselves explain the inconsistent pattern
of choices across the battery of games in our experiment. For example,
sometimes the subject may “appear” altruistic, in one choice, and then
“appear” greedy in another choice, even though the incentives are identical
and are stated identically for the two tasks. Some subjects are altruistic some
of the time, other subjects are altruistic most of the time, and some subjects
are never altruistic. At best, we need amendments to game theory that
differ for each and every game and for each individual. This would make it
difficult, or impossible, to provide a general explanation of behavior that is
built on game theory.
Game theoretic predictions about behavior depend on the assumption
that beliefs and choices are aligned. Researchers rarely possess knowledge
of the actual beliefs of subjects. But our within-subject experiments allow
us to test beliefs, and we find that for individual subjects, there is routine
and ubiquitous inconsistency across choice and beliefs (see Appendix and
McCubbins, Turner, & Weller, 2012). We demonstrate that subjects’ beliefs
are often inconsistent with equilibrium predictions, which has not been
widely appreciated. Our findings also show that these deviations are not
consistent; they depend on the specific setting and task. These deviations
are so pervasive and so various even within a single subject that is seems
unwarranted to refer to them as deviations. On the contrary, consistent “Nash
behavior and beliefs” appear to be remarkable deviations from human
cognitive patterns and human behavior.
ADVANCE DIRECTIVE FOR BEHAVIORAL GAME THEORY:
DO NOT RESUSCITATE
Our results show, as has often been shown, that subjects deviate from the predictions made by classical equilibrium analysis in game theory. We emphasize that (i) subjects often deviate from these predictions, but that (ii) for
the vast majority of subjects, their deviations are themselves not consistent
even across similar tasks, and (iii) there is large variance in how different
subjects choose for any individual task. Moreover, we show (iv) that individuals’ beliefs about other subject’s choices or beliefs do not support classical
Nash equilibrium strategies, and (v) that there is large variance between subjects and among a single subject’s beliefs from task to task. In addition, we
show that individuals do not hold common beliefs about game strategy or
deviations from equilibrium. Individuals’ beliefs seem to be specific to particular settings and not generalizable from one setting to the next. Indeed,
it may be misleading to refer to these patterns of action and belief as “deviations” at all. There are no consistent deviations from classical equilibrium
concepts, and thus there is no general behavioral fix. There are about four

Against Game Theory

9

dozen deviations from classical game theoretic predictions identified in the
literature. We find that the same individual subject will be deviating from
game theoretic predictions in as many ways as there are tasks in our experiment and that across all subjects in our experiment we see a great variability
from one subject to the next in the pattern of deviations. It is unsurprising, for
example, that some subjects are altruistic in some settings. It is unsurprising
that we find that some fraction of the subjects are altruistic for one or another
task. It is more surprising that subjects are altruistic in one task and then
not altruistic when offered the identical incentives again later on. All these
different variations of course interact with each other, giving a complex and
unpredictable landscape of complex variation running over individuals and
groups. Thus, adding behavioral assumptions to the general model of cognition within game theory cannot make these general models more suitable
for predicting behavior.
We have shown further that the protected core of game theory—the
unrecognized cognitive model, or Theory of Mind (McCubbins et al., 2012),
of noncooperative game theory—fails repeatedly in hypothesis testing. The
assumptions about human cognition that are part of game theory, including
the predictions of classical game theory and its refinements, are at odds with
what we know about actual human cognition. This is no surprise, because
the equilibrium concepts were not constructed based on how actual humans
think, reason, or make decisions. We do not yet see a way forward to creating
a behavioral game theory that offers meaningfully generalizable predictions.
Accordingly, our advance directive would say: Do Not Resuscitate.
THE NEXT STEP
What are the alternatives to game theory, both classical and behavioral? What
possibilities are there for forming testable hypotheses about interdependent
decision-making?6 Within cognitive science, there are a number of lines of
research about how actual human beings make actual decisions, several of
them reviewed by Turner (2001). These lines of research in cognitive science
have had virtually no consideration inside economics. Here are a few of them:
Variation Across Domains and Situations. Entire subfields of cognitive science
are dedicated to the ways in which human thought varies across different
domains and situations. Given basic considerations of evolutionary development and fitness, there is no reason to assume a priori that the way a human
6. Another way in which behavioral game theory has sought to account for ubiquitous deviations
from game-theoretic predictions is to add a random factor to human decision-making. One such prominent approach is “quantal response equilibrium” (see McKelvey & Palfrey, 1995). But it is largely impossible to put quantal response equilibrium to the test as almost any pattern of behavior is consistent with its
predictions (see McCubbins et al., 2013), especially when it is expanded to “heterogenous quantal response
equilibrium” (Rogers, Palfrey, & Camerer, 2009).

10

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

being thinks and acts with respect to food, mating, entertainment, and so
on would follow the same patterns or principles of reasoning and decision.
All models of game theory, classical and behavioral, assume the opposite,
namely, that although people might have different preferences with respect
to these different domains, their patterns of reasoning and choice must be
uniform across them. Game theory models two situations as identical if they
have the same game structure, regardless of the content. It does not matter,
for example, that the “Stag Hunt” game might concern growing vegetables or
killing soldiers. To a cognitive scientist, or maybe just to anybody other than
a game theorist, that approach looks like a nonstarter. It certainly should be
discarded as an assumption.
Learning. Entire subfields of cognitive science are dedicated to the various mental operations involved in learning, and to the study of how human
thought and action depend on the highly flexible and powerful learning for
which human beings are equipped. To give one example, cognitive science
routinely considers the power of analogy or blending: one remembers a previous specific situation, perhaps in childhood, or from a biography, or even
from a science fiction novel, and remembers, too, its outcomes; one then uses
those concepts and knowledge to inform one’s understanding and decisions
in the present specific situation. These traditions in cognitive science have
no status inside game theory, even though they provide a basis for hypotheses and tests about decision-making. Indeed, the validity of measuring such
powers of analogy and blending is so unquestioned in Western culture that
assessments of this ability are used as part of the process of deciding who has
what IQ and which applicants to college should be admitted.
Complexity and Nonlinearity. The world is rich, and in the typical situation,
actors are engaged in simultaneous games that overlap. In life, any action
is usually a move in many different games. Strategies to maximize expected
utility over all these games are typically nonlinear. In principle, the output of
any subgame of any game can be input to any subgame of any other game.
Game theory by contrast assumes a partitioning of thought and action to tiny
scripts of activity that are pretty much separate from all others. This assumption could be discarded.
Adaptive Behavior. In the typical situation, people are adaptive: their first and
strongest disposition is often not to play the game but to reinvent it, change
it. Their decisions can be driven by attempts to change the game from the
outside. Game theory leaves no room for this normal and routine thought
and behavior.
Construal. Cognitive science routinely investigates our rich capacities for
differing construals of the same given material. “The mountain range runs
from Canada to Mexico” and “The mountain range runs from Mexico to
Canada” deal with the same stuff but call for quite different emphases

Against Game Theory

11

and viewpoints. They also both call for conceptualization by using the
idea of motion (“runs from … to”), even though in some sense we think
that no motion is involved. Construal is a crucial part of interdependent
decision-making, because actors try to reconstrue history and to get other
actors to do the same. In the typical situation, actors work at conceptual
reinterpretation of the history of play, so as to persuade other actors that the
value and status of a past action must be changed, and further, to persuade
them that the action led to nodes different from those to which it was once
thought to lead. Conceptually, the history of the game is not fixed. Game
theory assumes the opposite.
What’s Up? Actors must operate in general without knowing what game
they are in, and the question always arises, who has the authority to recognize and establish the game being played? Actors attempt to influence other
actors’ thoughts about the game being played.
Identity. Cognitive science routinely considers the work people do to
construct an identity for themselves, and to carry it and vary it appropriately
from situation to situation. It may often be that the principle payoff in any
scripted activity is not the local payoffs but the actor’s concept of a personal
identity. When we enter different situations, different rooms, different
moments, what does the present offer by way of allowing us to construct an
identity? What looks like fatal inconsistency from the point of view of game
theory might look like fruitful experimentation, learning, and fluidity from
the point of view of actual human beings.
Within the social sciences, it has been shown that institutions (laws,
constitutions, auction mechanisms, common agency, families, friendships,
societal structures, and so on) serve to create not only incentives for choice
but also a set of shared mental models about players, actions, payoffs,
outcomes, and perhaps most important, information. This would imply that
the study of institutions might supply some of the cognitive grounding that
game theory is currently lacking. Yet another assumption of game theory
is that from knowledge about players, actions, payoffs, outcomes, and
information, one can derive strategies and equilibria. It is unknown whether
this is true, but what is clear is that institutions have already influenced
how subjects derive strategies and equilibria. People, developed within
institutions, are thus, when they enter our experiments, far from a tabula
rasa. There is little reason to imagine that the narratives that we can give
them in an experiment are strong enough to offer much hope of overcoming
that training within institutions. There is little reason to think that these
narratives in experiments would substitute for the purported “10,000 h” of
learning and practice needed to be successful at a given task. Accordingly,
the cognitive study of decision-making must include the study of learning
within institutions.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

In short, we think that the future for game theory, if there is one, would
come from a grounding in cognitive science, or more generally, in the analysis of how the cognitively modern human mind works, what its basic mental
operations are, and how they are deployed in situations. We know that strategic games such as chess arose very late in human evolution and even in
human culture and that people are very poor at such games in general and
must undergo extensive training in order to play them well. Such games of
strategy are perhaps the last place one should look for a model of human
decision-making generally. Game theory has placed itself into that cul-de-sac,
but there is no reason for that sterility and isolation. One could instead begin
with how actual human beings think.
APPENDIX ON EXPERIMENTAL DATA
This appendix provides details of subjects’ behavior in Trust, Dictator, and
Donation. First, on examining the play within the Trust Game, we find that
56% of the subjects as Player 1 sent money to Player 2. On average, they
sent $1.43, with a standard deviation of $1.70. On average, as Player 2, they
return $1.23, with a standard deviation of $2.29. Our emphasis is not on the
well-established deviance from classical predictions in Trust (indeed, the
standard deviation from our experiments is somewhat smaller than that
usually reported) but rather on the large variance in behavior both across
subjects in both tasks and by the same subject across different tasks. Only
1 of the 80 subjects who as Player 2 received $0 from Player 1 returned any
money to Player 1. Of the 100 subjects who did receive money as Player
2, 62 returned something. The average returned for this subset is $2.22,
again with a large variance (the standard deviation is $2.71). Second, for
the 62 who as Player 2 returned money to Player 1 after receiving money,
only 40 sent money when they were the Dictator; and of those 40, only 29
sent money when they were in the role of Donor. Was a subject’s pattern
of deviation from classical equilibrium consistent? There are 42 subjects
who deviate from classical equilibrium as both Player 1 and Player 2 in
Trust. Of these 42, 33 also deviated as Donor and, of these 33, 26 deviated
as Dictator. We see that fewer than 15% of our subjects consistently deviate
from classical equilibrium concepts across these four tasks. In sum, by even
the most minimal definition of consistency, only 42% of our subjects either
consistently follow classical equilibrium concepts (specifically, “SPNE”)
or consistently deviate from them, in these four tasks. That is, a minority
of subjects have even the most minimal consistency from task to task. We
report on similar results in the study by Lucas et al. (2013).
We turn now to reporting on the often hidden and never-tested parts of
“equilibrium concepts” in game theory, that is, the assumptions regarding

Against Game Theory

13

subjects’ beliefs and knowledge. In the Trust Game, for example, the classical
SPNE prediction for both players is that they will send $0 for all tasks. Thus,
if our subjects hold beliefs that support SPNE, both Player 1 and Player 2
should expect the other person in each task to send $0. Further, they should
expect that the other player expects that they will send $0. (And so on ad
infinitum, they should expect that the other expects that they expect that the
other player will send $0, and so on.) When acting as Trust Player 1, however,
88 of 180 subjects bet, and thus can be thought to believe, that Player 2 will
return some money to them. Likewise, when in the role of Player 2 in Trust,
the majority of participants (112 of 180) believe that Player 1 will send them
more than the equilibrium amount of $0. Indeed, only 21% (38 of 180) hold the
“correct” SPNE beliefs and, as both Player 1 and Player 2, bet that the other
person will send nothing. (More elaborately, as the “other person” is always
that other subject with whom the subject has been randomly paired for that
specific task, only 21% of the players expect both when they are Player 1 and
later when they are Player 2 that the other subject with whom they have been
randomly paired for that particular game will send nothing.) In total, 58 of
180 participants bet when they are in both roles—that is, Player 1 and Player
2—that the other person will send more than $0. In general, participants do
not hold beliefs that support a SPNE.
Examining consistency of belief in more depth, we can ask, for example,
how many of the 180 subjects in our analysis consistently held beliefs that
support an SPNE? As Player 2, participants made guesses about Player 1’s
prediction of how much Player 2 would return, and only 92 of 180 made
guesses that support an SPNE. Of those 92, only 41 also held SPNE-consistent
beliefs as Player 2 when guessing how much Player 1 predicted that Player 2
guessed Player 1 would transfer. Of those 41, 33 were also SPNE-consistent
as Player 2 when guessing how much Player 1 would transfer. Of those 33,
29 were also SPNE-consistent as Player 1 when guessing how much Player
2 predicted that Player 1 guessed that Player 2 would return. Of those 29,
27 were also SPNE-consistent as Player 1 when guessing both (i) how much
Player 2 would return and (ii) how much Player 2 predicted that Player 1
would send. In sum, only 15% of our subjects consistently adhere to beliefs
that support an SPNE as Player 1 and as Player 2 in a single game, Trust.
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ssrn.2278029
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McCubbins, M. D., Turner, M., & Weller, N. (2012). The theory of minds within the
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GALE M. LUCAS SHORT BIOGRAPHY
Gale M. Lucas is currently a postdoctoral research associate at University of
Southern California’s Institute for Creative Technologies. She is also affiliated
with USC’s Marshall School of Business. Dr. Lucas earned her PhD in Social
Psychology from Northwestern University, where she was named a National
Science Foundation Graduate Research Fellow. She has taught at Northwestern University, Willamette University, and Western Oregon University.
MATHEW D. MCCUBBINS SHORT BIOGRAPHY
Mathew D. McCubbins is Professor of Political Science and Law at Duke
University, and Director of the Center for Democracy and the Rule of Law,
Duke School of Law. Web page with link to CV: www.mccubbins.us
MARK TURNER SHORT BIOGRAPHY
Mark Turner is Institute Professor and Professor of Cognitive Science at Case
Western Reserve University. He is the Founding Director of the Cognitive
Science Network; Co-Director of the Red Hen Lab; Founding President of
the Myrifield Institute for Cognition and the Arts; Fellow of the Institute
for Advanced Study, the Center for Advanced Study in the Behavioral
Sciences, the National Humanities Center, the John Simon Guggenheim
Memorial Foundation, the Institute of Advanced Study at Durham University, the Centre for Advanced Study at the Norwegian Academy of
Science and Letters, the New England Institute for Cognitive Science and
Evolutionary Psychology, the National Endowment for the Humanities,
and the Institute for the Science of Origins; Extraordinary Member of the
Humanwissenschaftliches Zentrum der Ludwig-Maximilians-Universität;
and External Research Professor of the Krasnow Institute for Advanced
Study. His research is presented at http://markturner.org
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16

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

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Against Game Theory
GALE M. LUCAS, MATHEW D. MCCUBBINS, and MARK TURNER

Abstract
People make choices. Often, the outcome depends on choices other people make.
What mental steps do people go through when making such choices? Game theory, the most influential model of choice in economics and the social sciences, offers
an answer, one based on games of strategy such as chess and checkers: the chooser
considers the choices that others will make and makes a choice that will lead to a
better outcome for the chooser, given all those choices by other people. It is universally established in the social sciences that classical game theory (even when heavily
modified) is bad at predicting behavior. But instead of abandoning classical game
theory, those in the social sciences have mounted a rescue operation under the name
of “behavioral game theory.” Its main tool is to propose systematic deviations from
the predictions of game theory, deviations that arise from character type, for example.
Other deviations purportedly come from cognitive overload or limitations. The fundamental idea of behavioral game theory is that, if we know the deviations, then we
can correct our predictions accordingly, and so get it right. There are two problems
with this rescue operation, each of them is fatal. (i) For a chooser, contemplating the
range of possible deviations, as there are many dozens, actually makes it exponentially harder to figure out a path to an outcome. This makes the theoretical models
useless for modeling human thought or human behavior in general. (ii) Modeling
deviations are helpful only if the deviations are consistent, so that scientists (and
indeed decision makers) can make predictions about future choices on the basis of
past choices. But the deviations are not consistent. In general, deviations from classical models are not consistent for any individual from one task to the next or between
individuals for the same task. In addition, people’s beliefs are in general not consistent with their choices. Accordingly, all hope is hollow that we can construct a general behavioral game theory. What can replace it? We survey some of the emerging
candidates.

INTRODUCTION
Scholars employ game theory to model interdependent decision-making in
bargaining, constitutional law, democratic stability, standard setting, gender
roles, social movements, communication, markets, voting, coalition formation, resource allocation, war, and many other domains. For a review, with
citations, see Lucas, McCubbins, and Turner (2013).
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.

1

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

Game theory has been widely discredited: many studies have demonstrated game theory’s mispredictions. People seem to be highly sensitive
to frame or context and biased in their strategies. They follow heuristic
decision-making. They are limited in their ability to reason and learn. Many
attempts have been made to create a behavioral game theory by adding a
correction for each of four-dozen odd mispredictions (see Lucas et al., 2013).
But the span of mispredictions is so great and so varied that building in
corrections for them produces a model that is computationally intractable
for actual human beings.
REVIEW: THE ELEMENTS OF GAME THEORY
What is a game? A game, theoretically, is defined by identifying the players,
the actions available to them, the information they have about the game,
when they have such information, what they know about what others
know or will know and when those others will know it, the strategies
available to them that define rules for what actions they will take in making
decisions, the payoffs that come with outcomes, the range of outcomes,
and “equilibria.” The acronym for these dimensions is PAISPOE: players,
actions, information, strategies, payoffs, outcomes, and equilibria. What is
an equilibrium? An equilibrium is a path of choices made by players in the
game—a path that could happen, given the dispositions of all the players
as defined in game theory. An equilibrium concept is a rule a player uses to
pursue an equilibrium path. There are a number of proposed equilibrium
concepts that players might use. They have names such as “dominant
strategy,” “Nash equilibrium,” “Bayesian strategy,” “correlated strategy,”
and “subgame perfect Nash equilibrium (SPNE).” The classic game theory
equilibrium concepts are “dominant strategy” and “Nash equilibrium.”
A pure-strategy Nash equilibrium concept, for example, is a combination
of actions for all the players according to which no player can benefit by
unilaterally deviating from his or her combination. For a review of types
of equilibrium concepts, see Maschler, Solan, and Zamir (2013). To be
generalizable, all of the attempts to model interdependent choice, classical
or behavioral, must assume that (i) people follow equilibrium strategies,
(ii) there are specific types of people who choose a generalizable strategy
over a class of tasks, or (iii) all people in performing a specific task choose
a generalizable behavioral strategy. Behavioral game theory is trying to
build a layer cake on top of game theory, by adding layers to the original
model. Each additional layer consists of a correction to the foundation. For
example, prospect theory would eliminate certain strategies associated with
disfavored bets.

Against Game Theory

3

But the number of adjustments needed to build a behavioral game theory
is so vast that it cannot yield generalizable models. The literature has proposed many adjustments in terms of bounds, biases, heuristics, and context
dependencies. This presents two problems for behavioral game theory. First,
experimental economists working in the laboratory and knowing that subjects make one or more of these adjustments are no longer in the position of
knowing subjects’ true payoffs: we know only the experimental economists’
view of the experimental earnings, typically thought to be the subjects’ earnings. What experimentalists do not consider is “context,” that is, factors such
as unobserved experimenter demand and framing. Second, and most important, under such adjustments, we do not know what the subjects believe.
Most games, especially those simple enough to be tested in the lab and simple enough that we can strip out most (if not all) of the effect of framing
and context, assume that subjects share common knowledge. Classical game
theory requires players to have correct and consistent beliefs. To have “correct beliefs” is to regard other players as following classical game theory and
to predict that they follow classical equilibrium strategies. Indeed, it is also
required that players know that other players know that they themselves
are following classical strategies and so on, ad infinitum. As Lupia, Levine,
and Zharinova (2010) note, the condition is even stronger, in that a classical
equilibrium concept “requires shared conjectures … . Common Nash refinements … continue to require that actors share identical conjectures of other
players’ strategies” (p. 106). This is part of what economists assume when
they accept that the players in a game share “common knowledge.” As Smith
(2000, p. 9) writes, citing two other winners of the Bank of Sweden Prize in
Economic Sciences in Memory of Alfred Nobel:
“The common knowledge assumption underlies all of game theory and much
of economic theory. Whatever be the model under discussion … the model
itself must be assumed common knowledge; otherwise the model is insufficiently specified and the analysis incoherent” (Aumann 1987, p. 473). Without
such common knowledge people would fail to reason their way to the solution
arrived at cognitively by the theorist. This is echoed by Arrow (1987) when he
notes that a “monopolist, even … where there is just one in the entire economy,
has to understand all these [general equilibrium] repercussions … has to have
a full general equilibrium model of the economy.” (p. 207)1

Nash showed that any two-player zero-sum game has an equilibrium and
it was later proved that finding this equilibrium is computationally tractable.
(A zero-sum game has fixed payoffs, where higher payoffs to one player
result in corresponding lower payments to other players). This was the
1. Smith here quotes a reprint of an original article by Arrow (1986).

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

appeal of noncooperative game theory: we could find equilibria that in turn
predict outcomes of interest. But, even in the case where there are only two
players and two actions, we cannot expect humans to solve non-zero-sum
games, as they are computationally intractable or infeasible, falling into the
class of computational problems identified as PPAD-complete2 (for history,
definition, and analysis, see Daskalakis, Goldberg, & Papadimitriou, 2009;
see also Daskalakis, Goldberg, & Papadimitriou, 2005; Chen & Deng, 2006).
The core problem for building a behavioral game theory is that, as we
add the biases, heuristics, and context dependencies suggested by decades
of research, we are implicitly increasing the dimensionality of the computational problem of finding an equilibrium. It may seem that building a
range of possible deviations into the model would help us build a better
model. Doing so requires the bold assumption that a given subject, when
faced, for example, with a series of non-zero sum games, deviates from
classical game theory in a way that is consistent from one game to the next,
and even from one choice to the next inside the same game. The result is
indeed a generalizable theory—perhaps a false theory, but one that is at
least generalizable. But for that theory to give us purchase on modeling
human thought or predicting human behavior, the deviations in beliefs and
therefore strategies, must—at a minimum—be consistent. They also must
be common knowledge: subjects will have no way to compute consistent
strategies if the way in which subjects deviate from strategies is private
information belonging to only the capricious subject and unknowable to
other subjects. That is the bedrock on which the rescue operation for failed
game theory must be built. Our evidence, however, like all other evidence
of which we are aware that touches on this point, shows that this presumed
bedrock does not in fact exist.
NEW FINDINGS
RESEARCH DESIGN
There are two important new features of our experimental design. First,
we created a battery of tasks. Our experiments use a battery of up to 17
2. PPAD stands for “polynomial parity argument on directed graphs.” It is a complexity class regarded
as exceptionally difficult. In computational complexity theory, a problem X is called hard for a complexity
class C if any problem in C can be reduced to X, which implies that no problem in C is harder than X, as
a solution to X provides a solution to any problem in C. If X is both hard for C and in C, then X is called
C-complete. A problem that is C-complete is the hardest problem, computationally, in C, or rather, there
is no harder problem in C. A PPAD-complete problem is in principle “so hard to calculate that all the
computers in the world couldn’t find it in the lifetime of the universe” (Hardesty, 2009). Accordingly, it
is difficult to imagine that human beings playing a game would seek solutions by trying to perform such
a computation. “By showing that some common game-theoretical problems are so hard that they’d take
the lifetime of the universe to solve, Daskalakis is suggesting that they can’t accurately represent what
happens in the real world” (Hardesty, 2009).

Against Game Theory

5

games, several of which we constructed by modifying the standard form of
well-known games such as “Prisoner’s Dilemma,” “Public Goods,” “Stag
Hunt,” “Ultimatum,” “Trust,” “Chicken,” and “Dictator.” The purpose of
our modifications is to minimize or eliminate the framing of the game and
to present the games, to the extent possible, as starkly as they are defined
in prominent textbooks in game theory. For details, see Lucas et al. (2013).
We emphasize that, unlike the typical method of running experiments in
psychology and economics, where subjects face the same task repeatedly,
our method presents subjects with a battery of tasks. In addition, unlike
psychology experiments, where subjects are typically paid in the form of
satisfying a course requirement, and unlike economics experiments, where
subjects are typically paid at random for only one of the two to three dozen
repetitions of the task, our subjects know that they are paid in cash according
to every action they take in every task.
Second, we added prediction markets, based on Plott and Roust (2005) and
Wolfers and Zitzewitz (2004). In these prediction markets, subjects could earn
additional money by placing bets on the choices that were made by the players with whom they were matched and in many cases by placing bets on
the collective choices of all subjects who had played the game during previous runs of the experiment. We create a market, specifically a betting market,
where we invite subjects to bet on other players’ choices. We quiz the subjects on the betting procedure so that we could both motivate them to work
hard to understand what the bets entailed and also to measure each subject’s
compliance with respect to the betting tasks. The subjects were paid if their
bets regarding the other player’s actions were accurate and they were given
a chance to also double down on their bets if they felt confident about their
predictions. Subjects understood that they can earn this extra money from
betting, and how much for each bet. For example, in the Trust Game, there
are two players randomly paired—Player 1 and Player 2; both start with $5;
Player 1 can select any number of dollars from 0 to 5 to give away; those
dollars are taken from Player 1, tripled by the experimenters, and given to
Player 2; after receiving them, Player 2 has the opportunity to transfer back
any number of the dollars that Player 2 has in total, including Player 2’s original $5. At this point, Player 2 may have any number of dollars between 5
and 20. We ask Player 1 to guess how many dollars Player 2 will return.
Later, but before Player 2 learns Player 1’s choice, we ask Player 2 to guess
how many dollars Player 1 selected to give away. We also ask Player 2 to
guess how much Player 1 predicted Player 2 would transfer back to Player
1. After Player 2 learns Player 1’s choice, we then ask Player 2 to guess how
much Player 1 predicted that Player 2 would return. All players know that a
player earns $3 for each correct guess and nothing for a guess that is wrong.
The questions we ask vary slightly for each task, but, as an example, here

6

EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

is an exact question we ask Player 1 in the Trust Game: “How much money
do you guess the other person transferred back to you? If you guess correctly, you will earn $3. If not, you will neither earn nor lose money.” Players
know that, with one exception, they can never learn whether their predictions
(bets) were right or wrong and that subjects never have any information about
other subjects’ guesses (bets). The exception is the rare case in which Player
2 in a sequential game, such as Trust or Ultimatum, must know Player 1’s
choice in order for Player 2 to understand Player 2’s situation and payoffs.
For example, Player 2 in Trust must be informed of how many dollars Player
1 chose to give away, if Player 2 is going to know how many dollars Player
2 has and therefore what the possible actions and payoffs are. Even then, the
delivery of this information to Player 2 and Player 2’s subsequent choice are
postponed to the last set of choices a Player makes, so as to have no effect
on previous choices. Payments to subjects are made in a lump sum, without
accounting or explanation, individually, anonymously, and privately, when
the experiment is completed.3 We do this to eliminate any opportunity for
subjects to make inferences about other players’ choices (either individually
or collectively), and subjects know this before they make any of their many
choices in the extensive battery. For details on these prediction markets in a
range of games, see Lucas et al. (2013).
RESULTS
Across our battery of tasks, our results verify decades of research demonstrating that subjects do not follow game-theoretic predictions. Consider a
traditional Ultimatum Game. According to Andreoni and Blanchard (2006,
p. 307), this game “has come to symbolize the power” of classical game theory and “its utter failure in practice.” In this “bargaining game,” a “proposer”
makes a take-it-or-leave-it offer to a “responder,” who then accepts or rejects
the offer. The classical equilibrium prediction is that if players care only about
their own monetary payoffs, then the responder will accept any positive offer
the “proposer” makes. (More technically, not counting the “endowment” of
dollars with which players begin—in our experiment, for example, the proposer begins with $10 and the responder with $0—if we assume that players
care only about the money they earn, then the Nash Equilibrium prediction
for the responder is that the responder will accept any positive offer the “proposer” makes; and the Nash equilibrium prediction for the proposer is that,
knowing that the responder will accept any positive offer, the proposer will
reason by backward induction to choose the smallest possible positive offer
allowed by the game.) Despite the stark framing of our experimental tasks,
3. Except for on time show up fees that were paid to all subjects and except for payments for the first
quiz relating to general experimental instructions.

Against Game Theory

7

our results generally replicate what others have found about the poverty of
classical Nash equilibrium predictions (see Camerer, 2003). For example, only
slightly more than 6% of our subjects chose the classical strategy when they
play the Ultimatum Game.
But the question we focus on with our battery of experimental games is,
when players “deviate” from the classical strategies, do they do so consistently? The answer is no, and if there is no consistency, then the modifications
to classical game theory cannot provide a generalizable model of behavior.
For example, the first half of our Trust Game is exactly like a game that we
call “Donation”: a given subject as Player 1 in Trust is in exactly the same
payoff and action situation as he or she is when he or she is the Donor in
Donation. Accordingly, we can measure whether a given subject is consistent
across these two situations. In addition, the second half of our Trust Game is
exactly like our Dictator Game: a given subject as Player 2 in our Trust Game
faces the same incentives and action possibilities as he or she faces when he
or she is the Dictator in our Dictator Game.4 We thus can measure whether a
given subject is consistent across these two situations. In addition, all subjects
completed a Trust Game where they made choices as Player 1 and also completed a Trust Game where they made choices as Player 2. We therefore can
examine the consistency of a given subject’s behavior within a game, namely
Trust (see Lucas et al., 2013, for details).
Our findings show that in Trust, there is large variance in behavior across
subjects in the role of Player 1 and also in the role of Player 2. (We discuss
findings in more detail in the Appendix.)
They also show that there is large variance in behavior by the same subject
in those two roles. We expected to find that subjects deviate from predicted
behavior for each and every task, but, for example, our results show much
more than that for Trust, Dictator, and Donation: fewer than 15% of our subjects deviate consistently from classical equilibrium concepts across the four
tasks involved in those games.5 For these four tasks, by even the most minimal definition of consistency, only 42% of our subjects either consistently
follow classical equilibrium concepts or consistently deviate from them. That
is, a minority of subjects have even the most minimal consistency from task
to task. We report on similar results in Lucas et al. (2013).
This suggests that simple amendments to game theory, such as adding
social preferences of one sort or another, risk preference, or discovering each
subject’s individual level of experience or ability to undertake the reasoning
necessary to choose an optimal strategy, or the level of randomness in each
4. Of course, one difference remains, the Trust task is interactive, whereas the Dictator task is not.
5. That is, in making choices as Player 1 or Player 2 in Trust, in making choices in Dictator or Ultimatum, subjects sometimes deviate and sometimes do not deviate from classical Nash equilibrium predictions. Those that deviate do not always do so, and few subjects deviate on every choice and few never
deviate.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

individual’s choices, cannot by themselves explain the inconsistent pattern
of choices across the battery of games in our experiment. For example,
sometimes the subject may “appear” altruistic, in one choice, and then
“appear” greedy in another choice, even though the incentives are identical
and are stated identically for the two tasks. Some subjects are altruistic some
of the time, other subjects are altruistic most of the time, and some subjects
are never altruistic. At best, we need amendments to game theory that
differ for each and every game and for each individual. This would make it
difficult, or impossible, to provide a general explanation of behavior that is
built on game theory.
Game theoretic predictions about behavior depend on the assumption
that beliefs and choices are aligned. Researchers rarely possess knowledge
of the actual beliefs of subjects. But our within-subject experiments allow
us to test beliefs, and we find that for individual subjects, there is routine
and ubiquitous inconsistency across choice and beliefs (see Appendix and
McCubbins, Turner, & Weller, 2012). We demonstrate that subjects’ beliefs
are often inconsistent with equilibrium predictions, which has not been
widely appreciated. Our findings also show that these deviations are not
consistent; they depend on the specific setting and task. These deviations
are so pervasive and so various even within a single subject that is seems
unwarranted to refer to them as deviations. On the contrary, consistent “Nash
behavior and beliefs” appear to be remarkable deviations from human
cognitive patterns and human behavior.
ADVANCE DIRECTIVE FOR BEHAVIORAL GAME THEORY:
DO NOT RESUSCITATE
Our results show, as has often been shown, that subjects deviate from the predictions made by classical equilibrium analysis in game theory. We emphasize that (i) subjects often deviate from these predictions, but that (ii) for
the vast majority of subjects, their deviations are themselves not consistent
even across similar tasks, and (iii) there is large variance in how different
subjects choose for any individual task. Moreover, we show (iv) that individuals’ beliefs about other subject’s choices or beliefs do not support classical
Nash equilibrium strategies, and (v) that there is large variance between subjects and among a single subject’s beliefs from task to task. In addition, we
show that individuals do not hold common beliefs about game strategy or
deviations from equilibrium. Individuals’ beliefs seem to be specific to particular settings and not generalizable from one setting to the next. Indeed,
it may be misleading to refer to these patterns of action and belief as “deviations” at all. There are no consistent deviations from classical equilibrium
concepts, and thus there is no general behavioral fix. There are about four

Against Game Theory

9

dozen deviations from classical game theoretic predictions identified in the
literature. We find that the same individual subject will be deviating from
game theoretic predictions in as many ways as there are tasks in our experiment and that across all subjects in our experiment we see a great variability
from one subject to the next in the pattern of deviations. It is unsurprising, for
example, that some subjects are altruistic in some settings. It is unsurprising
that we find that some fraction of the subjects are altruistic for one or another
task. It is more surprising that subjects are altruistic in one task and then
not altruistic when offered the identical incentives again later on. All these
different variations of course interact with each other, giving a complex and
unpredictable landscape of complex variation running over individuals and
groups. Thus, adding behavioral assumptions to the general model of cognition within game theory cannot make these general models more suitable
for predicting behavior.
We have shown further that the protected core of game theory—the
unrecognized cognitive model, or Theory of Mind (McCubbins et al., 2012),
of noncooperative game theory—fails repeatedly in hypothesis testing. The
assumptions about human cognition that are part of game theory, including
the predictions of classical game theory and its refinements, are at odds with
what we know about actual human cognition. This is no surprise, because
the equilibrium concepts were not constructed based on how actual humans
think, reason, or make decisions. We do not yet see a way forward to creating
a behavioral game theory that offers meaningfully generalizable predictions.
Accordingly, our advance directive would say: Do Not Resuscitate.
THE NEXT STEP
What are the alternatives to game theory, both classical and behavioral? What
possibilities are there for forming testable hypotheses about interdependent
decision-making?6 Within cognitive science, there are a number of lines of
research about how actual human beings make actual decisions, several of
them reviewed by Turner (2001). These lines of research in cognitive science
have had virtually no consideration inside economics. Here are a few of them:
Variation Across Domains and Situations. Entire subfields of cognitive science
are dedicated to the ways in which human thought varies across different
domains and situations. Given basic considerations of evolutionary development and fitness, there is no reason to assume a priori that the way a human
6. Another way in which behavioral game theory has sought to account for ubiquitous deviations
from game-theoretic predictions is to add a random factor to human decision-making. One such prominent approach is “quantal response equilibrium” (see McKelvey & Palfrey, 1995). But it is largely impossible to put quantal response equilibrium to the test as almost any pattern of behavior is consistent with its
predictions (see McCubbins et al., 2013), especially when it is expanded to “heterogenous quantal response
equilibrium” (Rogers, Palfrey, & Camerer, 2009).

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

being thinks and acts with respect to food, mating, entertainment, and so
on would follow the same patterns or principles of reasoning and decision.
All models of game theory, classical and behavioral, assume the opposite,
namely, that although people might have different preferences with respect
to these different domains, their patterns of reasoning and choice must be
uniform across them. Game theory models two situations as identical if they
have the same game structure, regardless of the content. It does not matter,
for example, that the “Stag Hunt” game might concern growing vegetables or
killing soldiers. To a cognitive scientist, or maybe just to anybody other than
a game theorist, that approach looks like a nonstarter. It certainly should be
discarded as an assumption.
Learning. Entire subfields of cognitive science are dedicated to the various mental operations involved in learning, and to the study of how human
thought and action depend on the highly flexible and powerful learning for
which human beings are equipped. To give one example, cognitive science
routinely considers the power of analogy or blending: one remembers a previous specific situation, perhaps in childhood, or from a biography, or even
from a science fiction novel, and remembers, too, its outcomes; one then uses
those concepts and knowledge to inform one’s understanding and decisions
in the present specific situation. These traditions in cognitive science have
no status inside game theory, even though they provide a basis for hypotheses and tests about decision-making. Indeed, the validity of measuring such
powers of analogy and blending is so unquestioned in Western culture that
assessments of this ability are used as part of the process of deciding who has
what IQ and which applicants to college should be admitted.
Complexity and Nonlinearity. The world is rich, and in the typical situation,
actors are engaged in simultaneous games that overlap. In life, any action
is usually a move in many different games. Strategies to maximize expected
utility over all these games are typically nonlinear. In principle, the output of
any subgame of any game can be input to any subgame of any other game.
Game theory by contrast assumes a partitioning of thought and action to tiny
scripts of activity that are pretty much separate from all others. This assumption could be discarded.
Adaptive Behavior. In the typical situation, people are adaptive: their first and
strongest disposition is often not to play the game but to reinvent it, change
it. Their decisions can be driven by attempts to change the game from the
outside. Game theory leaves no room for this normal and routine thought
and behavior.
Construal. Cognitive science routinely investigates our rich capacities for
differing construals of the same given material. “The mountain range runs
from Canada to Mexico” and “The mountain range runs from Mexico to
Canada” deal with the same stuff but call for quite different emphases

Against Game Theory

11

and viewpoints. They also both call for conceptualization by using the
idea of motion (“runs from … to”), even though in some sense we think
that no motion is involved. Construal is a crucial part of interdependent
decision-making, because actors try to reconstrue history and to get other
actors to do the same. In the typical situation, actors work at conceptual
reinterpretation of the history of play, so as to persuade other actors that the
value and status of a past action must be changed, and further, to persuade
them that the action led to nodes different from those to which it was once
thought to lead. Conceptually, the history of the game is not fixed. Game
theory assumes the opposite.
What’s Up? Actors must operate in general without knowing what game
they are in, and the question always arises, who has the authority to recognize and establish the game being played? Actors attempt to influence other
actors’ thoughts about the game being played.
Identity. Cognitive science routinely considers the work people do to
construct an identity for themselves, and to carry it and vary it appropriately
from situation to situation. It may often be that the principle payoff in any
scripted activity is not the local payoffs but the actor’s concept of a personal
identity. When we enter different situations, different rooms, different
moments, what does the present offer by way of allowing us to construct an
identity? What looks like fatal inconsistency from the point of view of game
theory might look like fruitful experimentation, learning, and fluidity from
the point of view of actual human beings.
Within the social sciences, it has been shown that institutions (laws,
constitutions, auction mechanisms, common agency, families, friendships,
societal structures, and so on) serve to create not only incentives for choice
but also a set of shared mental models about players, actions, payoffs,
outcomes, and perhaps most important, information. This would imply that
the study of institutions might supply some of the cognitive grounding that
game theory is currently lacking. Yet another assumption of game theory
is that from knowledge about players, actions, payoffs, outcomes, and
information, one can derive strategies and equilibria. It is unknown whether
this is true, but what is clear is that institutions have already influenced
how subjects derive strategies and equilibria. People, developed within
institutions, are thus, when they enter our experiments, far from a tabula
rasa. There is little reason to imagine that the narratives that we can give
them in an experiment are strong enough to offer much hope of overcoming
that training within institutions. There is little reason to think that these
narratives in experiments would substitute for the purported “10,000 h” of
learning and practice needed to be successful at a given task. Accordingly,
the cognitive study of decision-making must include the study of learning
within institutions.

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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES

In short, we think that the future for game theory, if there is one, would
come from a grounding in cognitive science, or more generally, in the analysis of how the cognitively modern human mind works, what its basic mental
operations are, and how they are deployed in situations. We know that strategic games such as chess arose very late in human evolution and even in
human culture and that people are very poor at such games in general and
must undergo extensive training in order to play them well. Such games of
strategy are perhaps the last place one should look for a model of human
decision-making generally. Game theory has placed itself into that cul-de-sac,
but there is no reason for that sterility and isolation. One could instead begin
with how actual human beings think.
APPENDIX ON EXPERIMENTAL DATA
This appendix provides details of subjects’ behavior in Trust, Dictator, and
Donation. First, on examining the play within the Trust Game, we find that
56% of the subjects as Player 1 sent money to Player 2. On average, they
sent $1.43, with a standard deviation of $1.70. On average, as Player 2, they
return $1.23, with a standard deviation of $2.29. Our emphasis is not on the
well-established deviance from classical predictions in Trust (indeed, the
standard deviation from our experiments is somewhat smaller than that
usually reported) but rather on the large variance in behavior both across
subjects in both tasks and by the same subject across different tasks. Only
1 of the 80 subjects who as Player 2 received $0 from Player 1 returned any
money to Player 1. Of the 100 subjects who did receive money as Player
2, 62 returned something. The average returned for this subset is $2.22,
again with a large variance (the standard deviation is $2.71). Second, for
the 62 who as Player 2 returned money to Player 1 after receiving money,
only 40 sent money when they were the Dictator; and of those 40, only 29
sent money when they were in the role of Donor. Was a subject’s pattern
of deviation from classical equilibrium consistent? There are 42 subjects
who deviate from classical equilibrium as both Player 1 and Player 2 in
Trust. Of these 42, 33 also deviated as Donor and, of these 33, 26 deviated
as Dictator. We see that fewer than 15% of our subjects consistently deviate
from classical equilibrium concepts across these four tasks. In sum, by even
the most minimal definition of consistency, only 42% of our subjects either
consistently follow classical equilibrium concepts (specifically, “SPNE”)
or consistently deviate from them, in these four tasks. That is, a minority
of subjects have even the most minimal consistency from task to task. We
report on similar results in the study by Lucas et al. (2013).
We turn now to reporting on the often hidden and never-tested parts of
“equilibrium concepts” in game theory, that is, the assumptions regarding

Against Game Theory

13

subjects’ beliefs and knowledge. In the Trust Game, for example, the classical
SPNE prediction for both players is that they will send $0 for all tasks. Thus,
if our subjects hold beliefs that support SPNE, both Player 1 and Player 2
should expect the other person in each task to send $0. Further, they should
expect that the other player expects that they will send $0. (And so on ad
infinitum, they should expect that the other expects that they expect that the
other player will send $0, and so on.) When acting as Trust Player 1, however,
88 of 180 subjects bet, and thus can be thought to believe, that Player 2 will
return some money to them. Likewise, when in the role of Player 2 in Trust,
the majority of participants (112 of 180) believe that Player 1 will send them
more than the equilibrium amount of $0. Indeed, only 21% (38 of 180) hold the
“correct” SPNE beliefs and, as both Player 1 and Player 2, bet that the other
person will send nothing. (More elaborately, as the “other person” is always
that other subject with whom the subject has been randomly paired for that
specific task, only 21% of the players expect both when they are Player 1 and
later when they are Player 2 that the other subject with whom they have been
randomly paired for that particular game will send nothing.) In total, 58 of
180 participants bet when they are in both roles—that is, Player 1 and Player
2—that the other person will send more than $0. In general, participants do
not hold beliefs that support a SPNE.
Examining consistency of belief in more depth, we can ask, for example,
how many of the 180 subjects in our analysis consistently held beliefs that
support an SPNE? As Player 2, participants made guesses about Player 1’s
prediction of how much Player 2 would return, and only 92 of 180 made
guesses that support an SPNE. Of those 92, only 41 also held SPNE-consistent
beliefs as Player 2 when guessing how much Player 1 predicted that Player 2
guessed Player 1 would transfer. Of those 41, 33 were also SPNE-consistent
as Player 2 when guessing how much Player 1 would transfer. Of those 33,
29 were also SPNE-consistent as Player 1 when guessing how much Player
2 predicted that Player 1 guessed that Player 2 would return. Of those 29,
27 were also SPNE-consistent as Player 1 when guessing both (i) how much
Player 2 would return and (ii) how much Player 2 predicted that Player 1
would send. In sum, only 15% of our subjects consistently adhere to beliefs
that support an SPNE as Player 1 and as Player 2 in a single game, Trust.
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GALE M. LUCAS SHORT BIOGRAPHY
Gale M. Lucas is currently a postdoctoral research associate at University of
Southern California’s Institute for Creative Technologies. She is also affiliated
with USC’s Marshall School of Business. Dr. Lucas earned her PhD in Social
Psychology from Northwestern University, where she was named a National
Science Foundation Graduate Research Fellow. She has taught at Northwestern University, Willamette University, and Western Oregon University.
MATHEW D. MCCUBBINS SHORT BIOGRAPHY
Mathew D. McCubbins is Professor of Political Science and Law at Duke
University, and Director of the Center for Democracy and the Rule of Law,
Duke School of Law. Web page with link to CV: www.mccubbins.us
MARK TURNER SHORT BIOGRAPHY
Mark Turner is Institute Professor and Professor of Cognitive Science at Case
Western Reserve University. He is the Founding Director of the Cognitive
Science Network; Co-Director of the Red Hen Lab; Founding President of
the Myrifield Institute for Cognition and the Arts; Fellow of the Institute
for Advanced Study, the Center for Advanced Study in the Behavioral
Sciences, the National Humanities Center, the John Simon Guggenheim
Memorial Foundation, the Institute of Advanced Study at Durham University, the Centre for Advanced Study at the Norwegian Academy of
Science and Letters, the New England Institute for Cognitive Science and
Evolutionary Psychology, the National Endowment for the Humanities,
and the Institute for the Science of Origins; Extraordinary Member of the
Humanwissenschaftliches Zentrum der Ludwig-Maximilians-Universität;
and External Research Professor of the Krasnow Institute for Advanced
Study. His research is presented at http://markturner.org
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