Electronic copy available at: http://ssrn.com/abstract=1443980Electronic copy available at: http://ssrn.com/abstract=1443980

Irrational Beliefs, Rational Actions: Understanding subjects

behavior in a laboratory experiment

Mathew McCubbins,

University of California – San Diego, Department of Political Science

Nicholas Weller,

University of Southern California, Department of Political Science and

School of International Relations

Rational choice models are commonly used in political science. However, many

experimental results find humans do not behave as we would predict from simple rational choice

models. In this paper we report on the result of experiments in which subjects both play a

standard trust game and make predictions about other players in an experiment, thereby revealing

information about how they expect others to behave in the experiment. We find that conditional

on their beliefs, subjects play quite rationally in these games. The results suggest we need to

understand individuals’ beliefs and knowledge when we model behavior in experimental and

empirical settings.

Electronic copy available at: http://ssrn.com/abstract=1443980Electronic copy available at: http://ssrn.com/abstract=1443980

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Rational choice models are commonly used in political science, in part because they

make tractable the behavior of humans. Despite their relative simplicity compared to the real-

world, the models are far from simplistic. When models are used to generate predictions they

require us to make assumptions about at least the following factors: the source of individuals’

utility; their beliefs/information about the experiment and other subjects, and their cognitive

capacity. If we are wrong about any one of these assumptions our predictions will not match the

behavior we observe in either an empirical or experimental setting.

There are many experimental results from political science, economics and psychology

that find humans do not behave exactly as we would predict from simple rational choice models

even in highly controlled laboratory settings. These departures from predictions are a fruitful

starting place for further research, because they provide an opportunity to understand what

causes our models and behavior to diverge. A significant amount of research has worked on this

problem, usually with a focus on either alternative models of subjects’ utility functions or

incorporating cognitive constraints into our models. Another, less explored type of modification

involves what subjects believe about the likely actions of others.

In this paper we report on the result of experiments in which subjects both play a standard

trust game and make predictions about other players in an experiment, thereby revealing

information about how they expect others to behave in the experiment. We find that conditional

on their beliefs, subjects play quite rationally in these games. The results suggest that players

have quite different beliefs about the nature of the game than we typically assume in our game

theoretic models.

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In the remainder of this paper we proceed as follows. First, we review the reasons why

behavior may depart from predictions with a focus on the role of subjects’ beliefs. Second, we

propose a methodology to understand subjects’ beliefs in a trust game. Third, we present the

results of our experiments. Finally, we discuss the results and conclude.

1. Understanding why models and behavior disagree

The utility of rational choice or game theoretic models in political science has been

subject to intense debate. Scholars have argued that rational choice theory adds little value to

political science, because the theory fails to make meaningful contributions to the study of

politics (Green and Shapiro 1994). This critique has been quite influential, and has lead to a

variety of direct rebuttals regarding the utility of rational choice theory (Cox 1999; Ferejohn and

Satz 1994). In addition, scholars have argued that rational choice modeling can be improved by

incorporating research from cognitive science and psychology. In particular this research

suggests that we need to take account of what subjects know (McKenzie and Mikkelsen 2007),

information processing (Boudreau et al. 2009; Lupia and McCubbins 1998; Denzau and North

2000), motivated decision making (Taber and Lodge 2000), external constraints that affect

decisions (Smith 2008), and affect (see the various chapters in Neuman et al. 2008).

Lost in much of the debate about the utility of rational choice models and how to modify

them is a focus on exactly where humans differ from the assumptions of rationalist approaches.

Individual behavior that is inconsistent with rational choice models can come from at least three

sources. First, individuals may have utility functions that differ from the assumptions of rational

choice. 1

Second, individuals may possess cognitive limitations that prevent them from

1 A number of results in experimental economics suggest that subjects make decisions

that are often inconsistent with standard models of decision or game theory (Holt and Goeree

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processing information in the ways that we often assume (i.e. Simon 1957). Third, individuals

may possess different beliefs about the game or about the other relevant actors than we assume

they possess, which may lead them to behave differently than predicted even if they are utility

maximizing and fully rational. More work has focused on how the first two factors can influence

behavior; therefore we focus in this paper on how this third aspect can lead to observed behavior

that deviates from standard predictions. We present the results of an experiment designed to

elicit subjects’ beliefs about the other actors in a game setting. This allows us to examine a

particular component of rational choice analysis –whether or not individuals, conditional on their

beliefs, behave rationally.

Subjects’ beliefs about others are important to understand, because our predictions rely

on the fact that the modeler knows how actors understand other players and the game. In this

paper instead of focusing on whether actors have a utility function similar to the standard one

assumed in economics and political science, we investigate whether individuals can accurately

predict the actions of others and if there are any systematic biases in individuals’ predictions

about others. If subjects have beliefs about either the experimental task or other subjects that

differ from the assumptions used in our predictions, we may observe non-equilibrium behavior

that is not caused by subjects’ utility function.

2001; Camerer 2003).1 In economics, the dominant response to these findings has been to

suggest modifications to standard utility theory. The modifications include at least the following:

risk aversion (Kahneman and Tversky 1979; Rabin and Thaler 2001), inequality aversion

(Engelmann and Strobel 2004), and altruism (Eckel and Grossman 1996). All of these

approaches attempt to model behavior by modifying the utility function that underpins decision

making and behavior.

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Psychologists have pointed out that subjects often seem to violate normative rules of

decision making, in particular subjects make mistakes due to their prior beliefs and the

overweighting of joint presence of variables. McKenzie and Mikkelsen (2007) show that subject

decision making is remarkably consistent with a Bayesian perspective in which subjects’ priors

and the joint presence of rare events is more informative than their joint absence. These results

remind us that subjects are not empty vessels, and they come to experiments with their own

knowledge and beliefs, and unless we account for these beliefs we may misinterpret their

decisions in the lab.

Another reason that subjects may deviate from standard game theoretic predictions is due

to cognitive limits. The theory of level-k reasoning serves as a way to relax standard game

theoretic assumptions about individual’s cognitive capacity (introduced by Stahl and Wilson

1994, 1995, but the concept has since been used by many others such as Costa-Gomes and

Crawford 2006). The level-k reasoning approach allows individuals to differ in both their own

reasoning ability and in how they model the reasoning used by other players in the game. If

subjects have limited ability to predict others behavior and then to understand how others

behavior will affect their incentives we may observe systematic violations of game theoretic

models due to cognitive constraints.

Another possible explanation for subjects’ behavior is that they have different beliefs

about other subjects in the experiment than we typically assume.2 Although beliefs about others

are often central to game theoretic models, there is little or no agreement about how to measure

those beliefs. Rather, scholars typically observe subjects decisions and then infer something

about subjects’ beliefs, but this requires making a number of assumptions about the relationship

2 Beliefs can come from a variety of sources and may be learned or “innate.” For an interesting model of beliefs and

understanding of others see Myagkov and Orbell (2006).

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between behavior and beliefs. For instance, if a subject passes money in a trust game do we

conclude that they have a utility for things other than money (inequality, altruism, etc) or do we

conclude that subjects’ beliefs about others differ from what we assume in our theoretical

predictions? Both explanations may be consistent with the observed data and it is unclear how to

differentiate between the alternative explanations within the confines of the existing data.

Burnham et al. (2000) manipulate people’s perceptions of others in the experiment by

changing the words used to describe other subjects. They report that when they label subjects as

“partners” in their experiments subjects are more trusting and trustworthy than if the protocol

labels other subjects as “opponents.” Individuals act out of self interest in this perspective, but

they have contingent strategies based on perception of the other subjects. This suggests that

subjects use information to predict the likely behavior of other subjects and then condition their

behavior on beliefs about the other players in the game.

In another attempt to understand subjects’ expectations, Dufwenberg and Gneezy (2001)

have subjects make predictions about others in a “lost wallet” game to determine how

expectations about possible earnings in the experiment are related to subjects’ decisions. They

find that subjects are less likely to return the wallet as the amount contained in the wallet

increases, but still those who forego “taking” realize that they are likely to earn less money by

not taking the wallet. Subjects whose wallets are returned to them in the experiment believe that

the more money contained in the wallet the more the person who returned it will expect a reward

for returning it; however, in practice there is no relationship between the amount in the wallet

and the amount allocated to the person who returned it.3 In this setting the subjects’ beliefs

appear to only have a weak relationship to observed behavior.

3 In some ways this mirrors the common finding in trust games that there is little relationship between the amount a

Player 1 passes and the amount Player 2 returns.

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The preceding scholars did not provide incentives for correctly predicting others’ beliefs,

but there is some evidence that incentives affect the accuracy of beliefs. Gachter and Renner

(2006) find that predictions about others are more accurate in a public goods game when there

are incentives for being correct than when there are no such incentives. They also find that

conditional on beliefs, individual contributions do not vary based on whether beliefs were

incentivized. These results suggest that to understand subjects’ beliefs we should implement

incentive schemes that reward accurate predictions, but we also need belief-elicitation

mechanisms that do not affect the game theoretic equilibrium of the game so our predictions are

expected to be relevant even with the predictions added to the protocol.

A variety of scholars have implemented mechanisms to provide incentives for accurate

beliefs. Offerman et al. (1996) implement a mechanism in a public goods game where subjects

predict how many others will contribute to the public good, and they are paid based on the

accuracy of their predictions. Their mechanism uses a relatively complicated (from a subjects’

perspective) quadratic loss function for payoffs and requires individuals to assign a probability to

each possible number of subjects in the group that contribute to the public good. Croson (2007)

studies the relationship between subjects’ beliefs about others and their willingness to contribute

money in a public good experiment. She asks subjects to predict the number of other people in

the group who will contribute to the public good and then each person makes his/her individual

contribution. Subjects earn money based on how accurately they predict the number of others

who contribute to the public good game. She finds that subjects are more likely to contribute to a

public goods game when they predict higher numbers of others will do the same.

Through a variety of different research approaches these scholars have tried to measure

the effect that subjects’ beliefs and/or expectations are related to behavior in an experimental

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setting. The results all suggest that at least some of the non-equilibirum behavior in experimental

settings may be due to factors other than different utility functions. In this paper we build on this

approach to understating subjects’ decisions by implementing a mechanism for subjects to

predict the actions of other subjects in the experiments, and then analyzing the relationship

between predictions and actual behavior. We focus on the standard trust game which heretofore

has not been utilized in this type of research, but this game provides an environment to explore

how subjects in different roles predict the actions of others.

2. Investigating Subjects’ Beliefs via a Modified Trust Experiment

Our experiment combines a belief elicitation mechanism (described later) with the

standard trust game as developed by Berg et al. (1995). In this game the first player is given an

endowment of $10 and chooses how much, if any, money to pass to an anonymous second

player. The first player can keep any money he does not pass. The money that is passed is tripled

in value and the second player receives the tripled amount of money. The second player then

decides how much, if any, of the money to return the first player. The subjects know that they are

randomly paired to another subject for the game, and that they will never learn with whom they

played the game. In addition, our experiment was internet-based so subjects never saw each

other, and there was not an experimenter present to affect the subjects’ responses.4

We modify the standard trust game by implementing a novel mechanism to tap into

subjects beliefs about the other players in the game. To do this we ask the first player to make

4 Eckel and Wilson (2006) demonstrate that internet-based experiments may generate different behavior than

laboratory-based experiments. We certainly agree with this claim, but it does not materially affect our purposes in

this experiment. We are not interested in comparisons across experiments so we are not concerned (for now) with

the effect of the internet on subject behavior. In the future we plan to implement this prediction mechanism in

laboratory experiments as well that will help us to deterimine if subjects are more/less accurate in the laboratory

than the internet.

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two additional decisions in addition to how much of the $10 to pass to another subject.5 After the

first player decides how much money to pass to another player we then ask him or her to predict

how much the second player will return. If the prediction is accurate the subject earns $2, if the

prediction is within $1 of the actual return we pay the subject $1, and if the prediction is off by

more than $1 we do not pay him or her anything. We also ask the first player to predict how

much money another first player will choose to pass to a second player. The incentive scheme is

the same for this prediction.6 The predictions are always about anonymous other people so

subjects do not know anything about the other person whose behavior they are predicting.

We also add one prediction for the second player. Before the second player finds out how

much money the first player passed to him or her, we ask the second player to predict how much

the first player will pass. The incentive scheme for this prediction is the same as explained

earlier. In Figure 1 we outline the order of decisions for both first and second players in the

game.

Figure 1 about here

The methodology we employ is similar to some of previous cited scholarship on beliefs

in an experimental setting. Croson (2007) employs the most similar method to elicit subjects’

beliefs because her incentive mechanism is also quite simple, which we believe is a great benefit

in an experimental setting. The mechanism must be sufficiently simple enough that we can

ensure subjects’ predictions are driven by their beliefs and not by confusion. Our approach

shares some similarity with post-experiment surveys that ask subjects to describe the decision-

making that took place during the experiment. Unlike standard post-experiment surveys we

5 In some ways this modification is similar to the results in Dickson (2008) who has observers predict the behavior

of others in an experiment. 6 Although quite different from standard prediction markets (see Wolfers and Zietzwits 2004 for a review) we do

draw inspiration from them in the sense that we provide a financial incentive for subjects to predict correctly the

actions of others in the experiment.

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provide financial incentives for subjects to make accurate predictions about others, and we do

not ask subjects to rationalize their own decisions after making them. We believe that this is a

useful mechanism to determine subjects’ expectations about the task and other subjects. By

examining both the individual-level and aggregate-level predictions we can ascertain whether

subjects behave in a manner consistent with their predictions and whether in aggregate subjects

have beliefs that accurately predict the choices made by other subjects.

As we mentioned earlier we conducted this experiment over the internet. In doing so we

took advantage of the sequential nature of decisions in the trust game. We began by contacting

subjects who would be the first player in the experiment and had them make a decision about

how much of $10 to pass to an anonymous subject and make the two predictions described

earlier. We then contacted other subjects who would be the 2nd

players, and we randomly

matched 2nd

players to 1st players. Subjects in the role of 2

nd player made their predictions and

their decisions about how much money to return through the online interface. After all the first

and second players made their decisions, subjects were told where and when to show up to

receive their earnings. Many of these subjects had participated in other experiments with the

political science department, which helped to ensure our credibility with them.

2.2 What do predictions reveal about beliefs?

The primary goal of this experiment is to demonstrate a method that allows us to elicit

subjects’ expectations about an experiment in an attempt to help reveal whether or not subjects

make the same assumptions about the game and other subjects as we typically make as

experimenters. There are a number of possible hypotheses about subjects’ decisions in a trust

game that are possible to examine through this experimental methodology. In this section we

briefly present the hypotheses that we examine with our experimental approach.

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We quickly remind readers of the standard predictions in the trust game. The game

theoretic equilibrium to this game is that the first player will pass no money to the second player,

because the first player believes that the second player will not return any money and therefore

the first player will earn more money (assumed to be equivalent to utility) by not passing any

money. The second player will earn the most if she keeps all the money she receives, and

therefore the prediction is that second players will keep any money the first player sends to them.

The key assumption we investigate in these experiments is whether subjects have the beliefs we

assume them to have regarding others in the experiment.

Prediction 1: Subjects will be able to accurately predict others’ behavior. In particular, first

players should believe that second players will not return any money they receive.

Explanation: At either the individual or aggregate level subjects should be able to predict the

behavior of others who act as either Player 1 and/or Player 2. Standard game theoretic models

assume that individuals maximize utility and that in experimental settings money is equivalent to

utility. It is also assumed that all individuals are similar in this regard, and therefore subjects can

correctly predict others’ behavior, because they believe others attempt to maximize their

experimental earnings. Therefore, first players should believe that second players will not return

any money and second players should believe that first players will not pass any money.

Prediction 2: If subjects are altruistic, then

a. First players should pass money to second players, and this off-equilibrium behavior

by Player 1 should not be associated with a prediction that passing money increases

earnings if the behavior is driven by altruism.

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b. Second players will return some of the money they are passed.

Explanation: This prediction is based on the standard idea that altruistic individuals pass money

for reasons unrelated to personal monetary gain. For instance, behavior in which a first player

passes money and expects to make more money than had he or she kept all $10 is inconsistent

with the concept of altruism. On the other hand, if a first player passes money and expects to

receive less in return than he or she passed, then this is consistent with altruistic behavior. For

subjects in the role of second player any decision to return money is consistent with altruism.

Prediction 3: If subjects make their predictions based on a theory of mind in which everyone

else makes decisions similar to theirs, then subjects should predict that others will behave as they

behave.

Explanation: Even if subjects do not see themselves or others in the way suggested by game

theoretic analysis, subjects may simply predict that others will behave as they would behave.

This is consistent with a variety of psychological evidence that suggests individuals often believe

that others see the world similarly to how they see the world (Kuhlman and Wimberely 1976). If

this is true then we expect that first players will predict that others will pass similar amounts to

the amount they pass.

3. Results

Using an internet-based platform we collected the decisions of 38 individuals, which

form 19 unique pairs of players. The subjects were all undergrads at a large public institution.

The data from our experiments provides insight into the amount that Player 1s pass, the amount

the Player 2s return and each person’s predictions about others in the game.

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Figure 2 shows the distribution of the amount passed by Player 1 in this experiment

compared to the amount passed by Player 1s in the experiment of Berg eg al. (1995), which was

conducted in a standard classroom, laboratory setting. In our experiment Player 1s tended to pass

less money than in other experiments, which may suggest that these conditions moved players

closer to the game theoretic equilibrium.7

Insert Figure 2 about here

Moving beyond the basic decision by Player 1 to pass money we examine our first

prediction concerning the behavior of altruistic subjects. If Player 1s who pass money expect

that their decision will lead to greater total income for them, then they do not appear to be

altruistic. In addition, if Player 1s believe that passing money will lead them to make a profit,

then it suggests they believe Player 2 will return some of the money, which is also inconsistent

with standard assumptions that Player 2 will keep any and all money he receives from Player 1.

At the same time, the expectation of earning money in the game poses little challenge to standard

utility functions, because subjects are still trying to maximize income but their beliefs about

others are different than we typically assume.

In Figure 3 we present data on how much each Player 1 expected to earn in the

experiments (the x-axis represents the difference between the amount Player 1 predicted to

receive from the 2nd

player and the amount the subject sent to the 2nd

player). A positive number

indicates that Player 1 expects to gain money, and a negative number indicates that Player 1

expects to lose money. Of the 19 players whose data are depicted in Figure 3, fifteen of them

expect to either break even or make money in their exchange with Player 2. These results suggest

that subjects believe, and are willing to base financial decisions on the belief, that subjects who

7 Having subjects play on the internet removed much (perhaps all) of the possible “experimenter demand” effect that

is sometimes said to influence trust and other economic experiments.

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act as Player 2 will return enough money to make passing money profitable. This evidence is

generally inconsistent with the behavior of an altruist and also suggests that subjects in the role

of Player 1 do not believe Player 2 will keep all the money received.

Insert Figure 3 about here

An alternative way to interpret subjects’ predictions is that they are post-hoc

rationalizations of their behavior. There may of course be some element of this, but their

predictions are still interesting for two reasons. First, there are financial incentives for subjects to

predict correctly others’ behaviors, which should encourage subjects to offer accurate predictions

rather than simply rationalization. Second, even if every subject simply “makes up” a reason for

their behavior it is interesting that so many of the made-up answers are similar. In these

experiments nearly all of the subjects believe they will either make money or break even by

passing money to an unknown person. If it is post-hoc rationalization it is remarkably consistent

across the subjects in this experiment.

For Player 1 to profit from passing money, then the amount returned by Player 2 must be

greater than 1/3rd

of the tripled amount that he or she receives. Figure 4 displays on the x-axis the

difference between Player 2’s prediction about Player 1 and the actual amount received from

Player 1, and on the y-axis the figures shows the proportion of the tripled money that is returned

by Player 2. A positive number of the x-axis indicates that the predicted amount passed was

greater than the actual and a negative number indicates that less was passed than predicted. This

is one way to examine whether or not players’ expectations affect their behavior as suggested by

some prior research (Eckel and Wilson 2006).

Insert Figure 4 about here

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There are a few things of note in Figure 4. First, the vast majority of second players

return some money to the first player, which is consistent with the altruism as we outlined in the

Prediction 1.8 Second, Player 2’s are more likely to overpredict than underpredict the amount

that Player 1 will pass. Apparently, players in both roles overestimate how much money others

will forego in the experimental setting. Third, it is clear that only a few subjects in the role of

Player 2 actually return 1/3rd

of the money they are passed, which means that almost none of the

Player 1s break even after passing money. Despite the expectations of Player 1s that passing

money will increase their earnings, the actual results indicate that passing money usually leads to

earning less money than keeping the initial $10. Fourth, there does not seem to be a consistent

relationship between the proportion returned by Player 2 and the difference between the amount

Player 2 predicts she will receive and the amount she actually receives. This suggests either that

players’ expectations do not influence the proportion returned by Player 2 or that our prediction

task does not tap into players’ expectations about the amount they will receive.

Figures 3 and 4 both indicate that at the individual pair-wise level subjects do not

correctly predict others’ behavior. It may be, however, that the pair-wise comparison is

inappropriate and a better way to examine the data is to compare the overall distribution of

predictions to actual behavior.9 After all, since the pairing of any two subjects is random an

individual might predict the median tendency quite well but still be incorrect in predicting a

particular person’s behavior. Figure 5 shows a kernel density plot of Player 1s’ predictions and

Player 2s’ actual behavior. The most noticeable difference in the plots is that Player 1s predict a

significant number of returns greater than $5 but in practice Player 2s do not return more than $5.

8 It is worth separating behavior that is consistent with altruism from behavior that is driven by altruism. It may be

that those in the 2nd

player role act like altruists but do it because they perceive the experiment to be part of a larger

game and they are concerned with affecting future payoffs, which would be 9 For instance, in standard prediction markets we rarely examine individual-level behavior and instead focus on

aggregate decisions. This is analogous to us examining aggregate behavior in our experiment.

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Using a Wilcoxon rank sum test we can reject that the two distributions are the same at the 0.01

level. Even in the aggregate, therefore, it appears that Player 1s do not accurately predict Player

2’s behavior. This suggests that at least some of the behavior we observe in trust game may be

due to subjects’ inability to predict the actions of others rather than just the presence of utility

functions that differ from our standard assumption.

Insert Figure 5 about here

In predicting the behavior of other subjects it is possible that the internet-based platform

makes second players behave differently than they would behave in a non-internet setting.

Perhaps subjects can accurately predict others’ behavior as long as the other person is in a social

setting, but the anonymity of the internet causes second players to play differently than first

players predict. If this is the case, then the first players may predict the actions of others

incorrectly due to the internet-based nature of the experiment. To examine this possibility we

used the data from Berg et al. (1995) to examine whether our first players were more accurate

when decisions took place in a classroom setting. The simplest approach, in Figure 6, is to

simply compare Player 1’s expectations with Player 2’s actual behavior in these experiments and

in the original Berg et al. experiment.10

If subjects are better equipped to predict non-internet

based actions, then we should find that they are more accurate in their predictions of behavior

from the Berg et al. subjects.

Insert Figure 5 about here

Here we find that our Player 1’s predictions and the data from Berg et al.’s (1995) experiment

are much closer. In particular Player 1s in our experiment expected returns of more than $5,

10

The distribution of first player choices differs in our experiment and Berg et al.’s experiment, which may lead to

different behavior on the part of the second player. To examine this we modified which observations of 2nd

player

we included in the comparison. The comparison we discuss in this section is robust to that change.

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which is consistent with behavior from Berg et al.’s experiment. These results may suggest that

the internet platform modified Player 2’s actions in a way that made them difficult to predict.

We also collected data on the predictions of subjects who act as Player 2 in the trust

game. We asked Player 2s to predict how much money Player 1s would pass, because this is

another way to investigate Prediction 2 about subjects’ ability to predict others’ actions. Figure 6

displays a kernel density plot of the actual amount passed by all Player 1s in the experiment and

the amount Player 2s predict would be based. Although the two curves do not line up exactly we

cannot reject that they are drawn from the same distribution using a Wilcoxon rank sum test. The

biggest difference is that actual Player 1 behavior is distributed across the range of possible

amounts to pass whereas the predictions about Player 1 behavior have a high density around $2

and $3. However, this visual difference is not sufficient to find a statistical difference given the

existing sample size. These results suggest that Player 2s in the aggregate may be able to

accurately predict Player 1s behavior.

Insert Figure 6 here

The prior results suggest that subjects often fail to predict accurately the decisions of

subjects who are in a different role than the subject doing the predictions. To investigate our

third prediction about whether or not subjects can predict the actions of another person in the

same role, we asked Player 1s to predict how much money another Player 1 would pass to a

Player 2. This does not require subjects to think about how they would behave if they were in a

different role in the experiment. This aspect of the experiment serves as a way to test our

prediction about subjects’ ability to predict the behavior of others in their same role. Our

working hypothesis is that subjects make predictions based on the belief that others behave the

same as they behave. This might be considered a “You are Me” heuristic (Kuhlman and

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Wimberely 1976). In Figure 6 we display a kernel density plot of Player 1’s decisions and their

predictions about another Player 1. The two distributions look very similar and indeed a

Wilcoxon rank sum test fails to reject that they are drawn from the same distribution. The most

obvious visual difference is that Player 1’s pass amounts greater than $8 more frequently than

they predict others will do so.

Insert Figure 7 about here

Taken together these results suggest that both Player 1 and Player 2 often make

inaccurate predictions about the behavior of people in these experimental settings. This difficulty

in doing so may help us to understand why behavior is often out of equilibrium in simple

experiments, because subjects simply do not understand others in the way that we expect them to

do so in our models. These results also demonstrate that there is a vast amount we can learn

about subjects’ beliefs by utilizing information from subjects’ predictions about others. In

addition, these results suggest that using game theoretic predictions in empirical settings requires

careful consideration of the beliefs and knowledge of the actors being modeled.

4. Discussion and Conclusion

Debates about rational choice models in politics have generated a lot of claims and

counter claims, and there has been a variety of research to help us understand why these models

might fail to predict accurately human behavior. In this paper we have proposed a methodology

designed to help understand how subjects understand the environment in which we ask them to

make decisions. In particular, we are concerned with subjects’ predictions about others in the

experiment. The need to understand subjects’ beliefs arises from the fact that game theoretic

predictions require subjects’ beliefs about others to be the same as we model in our theories.

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However, experiments with human subjects have revealed that behavior often differs from our

game theoretic predictions. The explanations for the differences largely focus on modifications

of subjects’ utility functions to include non-material factors. An alternative, but less utilized,

explanation for non-equilibrium behavior is that subjects have different beliefs about how others

will behave than we assume in our game theoretic predications. If subjects’ beliefs differ from

what we assume in our models, then their behavior may deviate from equilibrium predictions

because of different beliefs or assumptions about what other believe or how others will behave.

In this paper we present a mechanism to help understand subjects’ beliefs about the likely

behavior of others in the experiment. By providing subjects with an incentive to predict others’

behavior we gain insight into what subjects believe others will do. Accordingly we can then

identify whether subjects’ actions correspond to their beliefs and whether subjects’ beliefs

correspond to the beliefs we assume in our predictions. We implement the prediction mechanism

into a standard experimental trust game.

Three findings are worth reiterating. First, subjects who are first players in the trust game

predict that passing money will be financially beneficial (i.e., more will be returned than was

passed). Second, conditional on their beliefs, first players act in a manner consistent with money

maximization. Third, predictions by 2nd

players about 1st players are generally more accurate

than 1st players’ predictions about 2

nd players.

These results suggest that subjects often have beliefs that differ from our game theoretic

models. To understand their behavior, therefore, we may need to account for the difference

between subjects’ actual beliefs and our assumptions about their beliefs. These results also

suggest that some of the incongruous results from prior experiments may be a function of

subjects’ beliefs rather than different utility functions or cognitive constraints. Further work will

20

be necessary to understand the conditions under which non-equilibrium behavior results from

different beliefs as opposed to different utility functions or cognitive constraints. Our results

clearly do not suggest that rationalist models are useless; subjects pursue monetary gains but

their beliefs differ from the beliefs we often assume them to have. By highlighting an additional

mechanism that is central to rational choice modeling these results can assist empirical and

experimental work by highlighting the fact that individuals may not have the beliefs we assume

in our models, and when individuals’ beliefs differ from our assumptions it can cause us to

misunderstand behavior.

21

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24

Figure 1: Order of Decisions in Trust and Prediction Experiment

Player 1 decides how

much of $10 to pass to

Player 2 Player 1 predicts how

much Player 2 will

return

Player 1 predicts how

much another Player

1 will pass to a

Player 2

Player 2 predicts how

much Player 1 will

pass to him or her

Player 2 receives the

tripled amount from

Player 1

Player 2 determines how

much of the tripled amount to

return and gets to keep any

unreturned money

Player 1 receives the

money returned from

Player 2

25

Figure 2: Amount passed by Player 1 compared to amount passed in other trust games 0

.05

.1.1

5.2

0 2 4 6 8 10Dollars

P1 pass, this experiment P1 pass (Berg et al.)

26

Figure 3: Most Player 1s Predict They Will Earn Money

01

23

45

Num

ber

of P

eop

le

-1 0 1 2 4 5

Expected Earnings

27

Figure 4: Player 2s’ Expectation Do Not Appear to Affect the Amount They Return

0.1

.2.3

.4

Pro

po

rtio

n o

f T

riple

d A

mo

un

t P

layer

2 R

etu

rne

d

-3 -2 -1 0 1 2 3 4 5 6 7Player 2's Prediction Minus Actual Amount Received from Player 1

Player 2's Expectations Do Not Affect Amount Returned

28

Figure 5: Player 1s’ Predictions and Player 2s’ Actual Returns

0

.05

.1.1

5.2

0 5 10 15 20x

Player 1 Expected Return Player 2 Return (Berg et al)

Player 2 Actual Return

29

Figure 6: Player 2 Predictions about Amount Player 1 Will Pass

0

.1.2

.3.4

0 2 4 6 8 10Amount Passed

Amount P1 Passes Amount P2 predicts will be passed

Can’t reject that the two distributions are the same (t-test or Wilcoxon rank test)

30

Figure 7:Player 1s Believe That Others Will Make Similar Decisions to Theirs

0

.05

.1.1

5.2

0 2 4 6 8 10Amount Passed

Player 1 Pass Player 1 Predicts Another Will Pass