Download Mental Representation of Games, Categorization, and

Doctoral Program in Economics and Management
CIFREM, University of Trento
XXIII Cycle
Mental Representation of Games, Categorization, and
Similarity
Extended Research Proposal
Sibilla Di Guida
5 February 2009
Abstract
For nearly five decades, experimental economics has been based on the assumption of
bounded rationality. Violations of rationality have been studied in both individual and
interactive strategic situations. A few studies have hypothesized that bounded rationality
emerges because of errors and simplifications in the mental models agents develop to process
information. The aim of my thesis is to investigate the role of mental representations of games
in the choice process. I will first run an experiment to verify whether subjects playing
different roles in the same game develop different misrepresentations of that game. Secondly,
I will design a model that mimics the process of categorization that real agents use when they
confront complex environments. Lastly, I will run an experiment to verify whether agents
develop categories for strategic games and to identify which of the several characteristics of a
game is more “evident” for them.
Introduction
In recent years, empirical findings have raised several doubts about the assumptions
underpinning microeconomic theory, in particular agents’ full rationality and their complete
and correct understanding of the environment with which they interact. Lab experiments have
extensively shown that agents are unable to identify the optimal strategy in a large number of
situations, both individual and interactive (Camerer, 2003; Kagel and Roth, 1995). Most of
such studies start from the assumption that first agents analyze correctly a strategic situation
and gather information about it, then are unable to optimally elaborate these pieces of
information and develop the best strategy.
What has been rarely investigated is the possibility that non-optimal strategies are due
to an erroneous mental representation of the strategic situation, rather than to a limited logical
capacity. A possibility is that agents first build a wrong mental representation of the strategic
situation and then choose optimally according to it. Devetag and Warglien (2008) have shown
empirically that this hypothesis is compatible with the data and that the role of mental
representation calls for careful investigation. In particular, an issue that has not yet been
explored in depth is the possibility that two subjects that are playing together can develop
differing mental representations of the same game, in relation to the roles played. This
situation may emerge particularly in games such as the “Trust Game”, where subjects have
“asymmetric” roles, but it may appear also in other types of sequential and simultaneous
games.
Another issue that has still to be investigated is the role played by categories in
interactive games. The theme of categorization is actually a subset of the issue of mental
representations, since it is an instrument to represent and store information about the world in
our minds. The importance of categories has been recently recognized in Choice Theory, but
mainly in relation to subjects’ individual mechanisms of choice. No attention has been paid to
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the possibility that subjects categorize interactive games and then choose based on the
categories they have previously built. Moreover the role of prototypes and analogies in the
categorization process also calls for further research.
My dissertation aims to fill these gaps by running a series of lab experiments and
developing a model of categorization. The model will replicate the mental mechanism that
subjects exploit in order to simplify the process of choice and reach a decision without full
information, in a finite time.
Literature Review
My thesis will be divided into two parts. In the first, I will investigate the role of mental
representation in games through a series of experiments. In the second, I will study
categorization in games, first designing a model of categorization, and then running some
experiments in order to test my hypothesis. Both parts are concerned with the problem of how
people represent and process information when playing games, but they refer to partially
different literatures. Neither topic has been deeply explored in economics, with a few
exceptions.
Mental representations in games
One of the main assumptions of game theory is that subjects are fully rational. In the case of a
strategic game, this implies principally that players are always able to develop an optimal
strategy that leads them to obtain the highest possible payoff. In order to select this strategy,
they must have a complete and correct understanding of the structure of the game, they must
know what are their partners’ objectives and, consequently, they are able to forecast their
partners’ strategies correctly. Since these assumptions are the same for all players, the direct
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consequence is that subjects should interpret the information in the same way. In other words,
it is assumed to be “common knowledge” of the characteristics of the game among subjects.
These assumptions leads to some severe implications and from the 1950s they have
been largely put to the test by a series of experimental studies that have illustrated how, in
many cases, subjects do not act as if they are fully rational. Starting from the Allais Paradox
(Allais, 1953), passing trough the Ultimatum Game (Güth et al., 1982), until arriving to the
Centipede Game (McKelvey and Palfrey, 1992), economists have identified many situations
in which players behave according to sub-optimal strategies, showing they do not behave in
conformity to rational principles of choice.
However in spite of the conflicting experimental evidence, the assumption of full
rationality is generally accepted. One of the reasons for which a lot of assumptions of
standard economics are still accepted (even if they have been proved not to be “universally
true”) is that they have been considered useful approximations of human behavior, even if not
precise and incontrovertible descriptions. Furthermore as all approximations they admit
counter-examples. Moreover, one of the classical critiques of experimentalists is that counterexamples are not sufficient and do not offer an alternative general theory of individual
behavior that could replace Expected Utility Theory (Kagel and Roth, 1995).
Even if the assumption of full rationality is generally accepted, some game theorists
have modeled bounded rationality in various ways. For my purpose, the approach taken by
Kreps (1990) is of particular interest. In his book, Kreps supports the idea that players
develop simplified and/or misspecified mental representations of the strategic situation in
order to choose their strategy. Kreps’s approach places subjects into a dynamic context where
they are involved in series of short-run strategic situations. Agents represent each of those
situations through some mental models that permit them to easily process the information and
to choose a strategy that is optimal according to the model. Since the models are
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simplifications and/or misspecifications, even if the choices are optimal according to them in
the short-run they can be non-optimal according to the true strategic situations. In the longrun, agents update their models thanks to the information and the experience gathered in the
previous periods, developing more refined mental representations.
According to this approach, subjects are supposed to be utility maximizers as
predicted by EUT. The novelty of this approach is that it allows the existence of bounded
rationality, which emerges in the phase of developing an imperfect mental model as a schema
for the true strategic situation. According to EUT, agents are able to process fully and
correctly the information necessary to find the optimal strategy. Accepting the existence of an
imperfect representation allows for the motivation of “irrational” behaviors without changing
the assumption of utility maximization. At this stage, three main questions emerge. Are actual
agents able to perceive correctly strategic situations, even in simple cases? Empirical findings
have in fact shown that behaviors do not conform to standard theory emerge not only in
complex but also in extremely simple environments, as in the case of the Ultimatum Game.
Many explanations based on other-regarding preferences have been provided for this kind of
phenomena (Rabin, 1993; Fehr and Schmidt, 1999), but no attention has been devoted to the
role that mental misrepresentations of the strategic situation play on this topic. Then how do
the mental representations differ from the true strategic situations? And lastly, do subjects
behave rationally according to their erroneous mental representations?
Even if economists have rarely taken into consideration the development of mental
models of strategic situations and the possibility of misrepresentations, psychologists have
long linked mental models with strategic thinking. As presented in Holland et al. (1986, 30),
First, a model must make it possible for the system to generate predictions even
though knowledge of the environment is incomplete. Second, it must be easy to
refine the model as additional information is acquired without losing useful
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information already incorporated. Finally, the model must not make requirements
on
the cognitive system’s processing
capabilities that
are infeasible
computationally. In order to be parsimonious, it must make extensive use of
categorization, dividing the environment up into equivalence classes.
Comparing Kreps’s and Holland et al.’s definitions of mental models, it is possible to find
some common elements. The first is that both expect to exploit the models in order to
generate predictions (or make choices); the model is then not only an instrument through
which to represent the world, but also a way to analyze and to interact with it. The second is
that they both define the model as a dynamic one that absorbs and modifies itself as new
information is obtained. These two aspects can be considered as the key characteristics of the
mental models of real strategic situations.
Two simple questions that come to mind at this point are: why should mental models
be so important and why do people need them? Mental models are not only important, but
fundamental and unavoidable. The environment in which we live surrounds us and sends us
several different kind of stimuli. Since it is something located outside us, the only way we
have to observe and analyze it is by constructing a stylized image in our brains. This image is
commonly called “mental representation”. What EUT asserts is that this representation is the
mirror image of the real world: it does not matter how complicated the environment is, agents
are always able to correctly represent it in their minds and to identify the best strategy for
every situation. Given these assumptions it is difficult (if not impossible) to explain the
“irrational” behaviors that have been detected in several experimental situations. Accepting
the existence of misrepresentation opens the possibility that wrong strategies are not due to
computational limits in the elaboration of a strategy, but rather to a rational choice for a
strategic situation that is not the original one. Devetag and Warglien (2008) propose that once
agents have constructed a wrong mental model, they are not able to find the optimal solution
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for the original strategic situation. What they will do is find the strategy that is the best with
respect to the mental model they have built.
Few economic studies have developed mental models. In an experimental paper,
Devetag and Warglien (2008) have examined how simplified mental models are connected to
task complexity. They also have investigated whether irrational strategies are related to the
mental representations. Starting from these objectives, the authors have designed an
innovative experiment where the structures of four classical games were reproduced through a
series of isotonic, antitonic, projective, and non-projective bi-orders, where bi-order is defined
a pair of order relations on a given set of elements. These games were a coordination game, a
game of conflict, a game of chicken, and a prisoner’s dilemma. During the experiments, the
agents had to choose from a set of objects of different shapes and colors a subset that satisfied
some given bi-orders. What emerged is that some bi-order structures are harder to represent
for players. More than 90 percent of the agents were able to satisfy the isotonic bi-order
(coordination game), while less than 50 percent correctly represented the non-projective biorder (prisoner’s dilemma). The authors have also investigated how these representational
errors affect the choice of strategy. They found that wrong representations were not casual,
but systematically simpler than the game that they represent, and that the choices of agents
were non optimal with respect to the original game, but consistent with their
misrepresentations. This article was one of the first attempts to investigate the role of mental
models in strategic situations. It has the merit of coping with the problem through a precise
and original experimental design, and the article gives a solid basis from which to start
working on the topic in more depth.
An aspect that has not been researched in this article is whether the misrepresentations
are unique for every game, or different subjects can have different misrepresentations. What
has been generally assumed is that the wrong mental representations are due to the structure
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of the games, which means that they should be identical for all the agents involved. A
possibility that has not been analyzed to date is that another aspect that affects mental
representations is the role played by an agent, so that subjects in different roles can have
different misrepresentations. This may imply that players may have differing representations
of the other players’ beliefs depending on their role in the game. More specifically, in games
such as the Ultimatum Game or the Trust Game. The logic behind this is that human beings
are much more prone to forgive themselves rather than others. I suspect that during the
process of developing a strategy, agents underestimate the impact of their choices in cases of
“bad” (such as greedy or unfair ones) choices, while they tend to overestimate it in the case of
“kind” (such as trusty or positive reciprocation) choices. There is the possibility that a player
can develop different misrepresentations of a game in relation to the roles held by each player,
to the effect his choices have on other players, and to the effects other players’ choices have
on his own payoffs. In my thesis I will investigate the existence of multiple
misrepresentations.
Categorization and similarity in games
The process of categorization has been thoroughly investigated both in psychology and in
economics. What is the aim of categories and when are they developed are two key questions
of a large research field. The most evident purpose of categories is to organize and classify
objects in order to exploit the information related to them in a more economic and efficient
way. Since every object is characterized by a huge number of attributes, it would be
extremely costly and inefficient to process all information related to it. Well-structured
categories provide the basis for focusing on the characteristics that are useful for the purposes
of agents, ignoring the “irrelevant” aspects.
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Does there exist only one type of category or do we associate this term with different
meanings? Rosch et al. (1976) affirm that categories have notable differences at different
levels of abstraction. As presented in Holland et al. (1986, 183), “ there is a “basic level” at
which it is natural to divide the world into alternative categories. This level maximizes the
perceptual and functional similarities among instances of the same category while it
maximizes the differences between instances of different categories”. Experimental evidence
has shown that for a large number of tasks, “basic level” categories are more efficient than
those subordinate or superordinate (Rosch et al., 1976).
Rather than categories per sè, some economists have studied the role of
categorization in choice theory. Some interesting theoretical works have modeled how an
optimal mechanism of categorization should be. One example is Fryer and Jackson
(2008, 1), who define an optimal categorization as one “… that minimize[s] the sum
across categories of within category variation”, a definition that they prove to be
(according to some minor conditions) equivalent to expected utility maximization. The
authors start from the idea that memory capacity is finite; in order to keep in mind a
series of objects with multiple attributes, agents group heterogeneous elements into
categories. The number of developable categories is also finite. Once the categories have
been created, agents build for each of them a prototype that summarizes the main
distinctive characteristics of the grouped objects, and they use these prototypes to
forecast the outcome of future situations they confront. According to the authors,
prototypes are characterized by several attributes, each of which is calculated as the
average of the corresponding attributes of all the elements contained in the category.
Some weaknesses of those models are that in order to obtain the categories complicated
calculations must be done, and every time a category is modified, so is its prototype.
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As mentioned before, this model belongs to the field of “optimal categorization
models” and mimics then not a real process of categorization but an ideal one. Minor
attention has been devoted to models that represent real processes of categorization.
What I aim to do in my thesis is to fill this gap by designing a “realistic” model of
categorization.
Another topic strictly related to categorization (and sometimes confused with it)
is that of similarity. The two main researchers of similarity are A. Rubinstein (1988) and
J. Leland (1994, 1998, 2001, 2006). In particular, Leland (1994, 2002) proposes a threestep model of strategic choice based on similarity judgment. In his works, the author
analyzes mainly the choice process among lotteries. In the first step, agents confront
different lotteries and choose that with the highest expected utility, then (step 2) if
subjects are unable to discriminate (as in the case where lotteries’ expected utilities are
too close) they compare possible outcomes and probabilities in terms of equality or
inequality. If also in this case they do not reach a decision, they pass to the last step
where they compare prizes and probabilities in terms of similarity or dissimilarity. If also
in this case it is not possible to choose an option, then the subjects choose randomly. The
model shows that, assuming people judge the various options searching for similarities
and dissimilarities of game payoffs and probabilities, it is possible to explain why the
axioms of expected utility and discounted utility are violated. The author also uses
experimental results to validate his hypothesis.
Even if the models proposed by Rubinstein and Leland have the advantage of
explaining a large number of violations of EUT without modifying the Von NeumannMorgenstern axioms, there are various points that are not well defined. The key
weakness is the concept of similarity involved. What is similarity in this context? When
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are two lotteries perceived as similar? The authors do not define the concept of similarity
adopted in the model, keeping it deliberately vague. What I propose is that similarity and
categorization are two strictly related, but distinct concepts. I suggest that objects (or
lotteries or games) are perceived as similar when they belong to the same category. The
process of categorization is then a compulsory requirement for the identification of
similarity, and allows for the unambiguous verification of the similarity of objects.
A large number of experimental economic studies exploits, in an indirect way, the
concept of similarity. In a series of papers, some scholars approach the transfer of
precedents’ problem by testing whether subjects play differently if they face a game
without precedent or after having played a related game. There is empirical evidence of
the positive influence of precedents (Devetag, 2005; Knez and Camerer, 2000). In those
works (similarly to what happened in Rubinstein’s and Leland’s models), there is not a
clear explanation of the meaning of the term related games. Are games similar if they
have the same number of possible choices for each player? Or the same kind of
equilibria? Or the same number of players? Or other characteristics? Devetag (2005) uses
two coordination games (critical mass and minimum effort) finding a significant effect of
precedents. In this case, the similarity among the games is defined by their structures; in
both cases players can choose between seven levels of effort. In Knez and Camerer
(2000), the subjects have to play two structurally different games (weak-link and
prisoner’s dilemma). Both games are used in the experiment in a three-choice or in a
seven-choice versions. What emerged is that transfer takes place more when the
similarity between two games is “superficial” rather than when it is “substantial”; i.e., it
is easier to have transfer among two three-choice (or seven-choice) games where one is a
weak-link and the other a prisoner’s dilemma, rather than among two structurally similar
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games (such as two prisoner’s dilemma games) but with a different number of possible
choices.
Many studies in economics have utilized the concept of similarity, taking for granted
that the meaning of the word is unambiguous. Starting from the idea that similarity is a
characteristic of objects grouped in the same category, I will devote some attention to the
process of the categorization of games by using an experimental approach. I want to
investigate which kind of games are naturally grouped together and which characteristics are
more “evident” for naïve players (number of possible choices, type of equilibria, and so on).
In particular, I want to verify if naïve agents are always able to distinguish among different
games.
Research Questions
The aim of this research is to investigate the role of mental representations and categories in
strategic games.
The first part aims to verify whether agents that are facing an interactive strategic
situation, but that play in asymmetric roles, have the same mental representation (or
misrepresentation) of the game. The possibility that subjects may have differing
understandings of the game has rarely been explored. On the one hand classical
microeconomic theory excludes the possibility that agents misunderstand the strategic
situation they are confronting, while on the other hand behavioralists have explored this idea
by analyzing the presence of systematic errors in the interpretation of games, but mainly
focusing only on searching for errors related to the nature of the game and not to the roles
played by the agents.
The second aim is to develop a model of categorization that mimics how agents
involuntarily and automatically develop categories in order to interact more easily and
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economically with their environment. In contrast with classical microeconomic theory, this
model will be based on the assumption that agents are not able to fully and correctly analyze
new objects and situations (it does not imply perfect knowledge). Agents’ knowledge will
increase with experience, i.e., with the number of times they observe a particular object
(situation). Since knowledge is strictly related to experience, the model assumes that agents
are not able to distinguish between similar objects (situations) in early stages, but their
capacity of observation will improve through time. When agents are not able to distinguish
between objects they group them as if they were the same, and in the model these groupings
are defined as “categories”.
The third aim will be to investigate empirically whether these categories play a role in
the choice process in games. The importance of categories has been widely explored both by
psychologists and economists in strategic situations where agents have to reach a decision
relative to their own behavior, but little attention has been paid to the effect of categorization
in games. The aim of this investigation will be to verify whether agents subject to a series of
games build categories in order to summarize the main characteristics of them, and act
accordingly.
Methods and procedures
The questions that have been raised above are related to each other since they investigate
different aspects of a common problem. Nonetheless, I will analyze them separately,
developing my research in three distinct phases.
In the first phase, I will verify whether subjects playing together have differing mental
representations of a game. The problem of differing representations can affect two aspects of
a game: the payoffs of the players and the structure of the game. Since I am interested in how
people actually behave, the best way to analyze their behaviors is empirically. A question that
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may arise at this stage is whether and how is it possible to analyze mental models, since by
definition they are implicit schemas. Of the two aspects, the study of the representations of a
game’s payoffs is the simplest. Payoffs are in fact easily quantifiable, and it is possible to ask
directly to subjects to identify numerical values that correspond to their perception of the
payoffs. The process of analyzing the mental models of a game’s structure is more complex.
Asking subjects to draw a schema of their mental models is not an useful technique since the
process of transferring the model from a mental to an explicit one is often difficult for
subjects, who tend to overcome the difficulties of expression through an excessive
simplification. It is more efficient to study the mental models of games’ structures in an
indirect way. An example is the experiment conducted by Cooper and Van Huyck (2003),
where the authors made subjects playing a series of 2X2 games both in normal and extensive
form. What emerged is that subjects actually do play differently when facing one form or the
other. Since the authors had strict methodologically control, it is plausible to affirm that the
differences are due only to the ways in which games were presented to players, rather to other
external factors. Even if this is not the authors’ interpretation, I consider it a case where the
role of mental models emerges. Since the games presented in both forms were the same, and
the subjects played in an “aseptic” environment, the fact that the same player applies two
different strategies can be linked to the subjects’ development of differing mental models.
This article is an example of how mental models can be investigated in an indirect way.
In order to investigate how agents perceive games’ payoffs in relation to the role they
play in the game, I propose to make two subjects play a series of different asymmetric games
in order to permit the emergence of differing interpretations of the strategic situation.
According to well-established methodologies, the experiments will be run with a set of
players grouped randomly in pairs, re-matching the subjects with a new partner at every
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round. The identity of the partner will remain unknown, and players will receive a reward in
relation to their performances.
Given the aim of my research, I am not interested in utilizing games with symmetrical
roles, since it is plausible to expect that all players of a game with symmetrical roles (as in
coordination games) come from a homogeneous population and consequently have the same
mental representation of it, even if they act differently. In a strategic situation like this, it is
plausible to consider possible differences among subjects due to cultural backgrounds, but the
analysis of them is beyond the scope of my research. I will then utilize games with
asymmetrical roles, as in the “Trust Game”, which has another characteristic that makes it
particularly well adapted for the purpose of this project: it can be represented as a sequential
game. In this type of game the choices of a player are the product of the previous choices of
the partner/opponent, and consequently the two players have different “power” over the final
payoffs. The extreme case is the “Dictator Game”, where the Receiver has no power at all and
can only take the money (if there is any) that the Dictator decides to give him. I consider it
plausible that players who face this asymmetry in power (and consequently observe the game
from a different perspective) can easily have different interpretations of the possible choices,
of the possible consequences their own choice produces on other players’ motivations and
choices, and of the payoffs that their own choices produce.
Another aspect that may produce differing misrepresentations of the game between
subjects is the contextualization of the game. Contextualization may have an effect similar to
that produced by sequentiality in games, inducing subjects to analyze the game from different
points of view and assigning them different “decisional power”. For this reason, I will also
test this aspect with both contextualized and non-contextualized games.
Up to this point the focus has been on the possible emergence of differing
interpretations of the payoffs of a game, but I intend also to introduce some other experiments
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in order to verify whether subjects develop different interpretations of the structure of the
same game.
In the second phase, I will develop a formal model that replicates the way in which
people create categories in order to comprehend and manage the situations they confront. I am
interested in designing this new model in order to fill an important gap in economic theory.
The problem of categorization has been neglected, particularly in relation to the behavior of
real agents; some optimal models have been produced, but almost no attention has been
devoted to models that mimic the true behavior of agents. I find this last topic particularly
intriguing and of great importance, since the capacity of perceiving and interpreting games
cannot be ignored when an efficient choice process is designed.
In classical microeconomic theory, it is assumed that agents have full knowledge of
the characteristics of the objects with which they are interacting. Similarly, it is assumed that
agents have a perfect knowledge of all the aspects of the possible actions they can take. These
assumptions do not appear to be realistic. Real agents have limited memory and a scarce
capacity to locate immediately all the most relevant characteristics necessary to take the best
possible decision. This is particularly true when they examine an object or face a situation that
is new to them. Assuming that it is impossible to completely comprehend a new situation, I
expect that knowledge about a particular object (or situation) increases with the number of
times an agent encounters it. If knowledge is augmented, so is the quality of the final choice.
Since, according to my model, knowledge increases over time and with experience,
agents are not always able to distinguish between different objects (or actions). For example
two objects (actions) that have some relevant characteristics in common can be confused as
being the same until the knowledge of them becomes deep enough to permit agents to identify
the differences. When more objects (actions) are grouped together and perceived as being
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equal, even if they are different, then I define the group as a category. Obviously, given these
assumptions the model groups the elements of the environment into a few categories, which
will be augmented over time. The longer the time (or the higher the number of objects
(actions) observed) the more detailed the categories will be and the more detailed the
categories the better the final choice.
Starting from these assumptions, I will propose a model that replicates the mental
mechanism of categorization that agents use in order to simplify their interaction with the
surrounding world. I want to clearly specify that my aim is to formalize a possible mental
mechanism, not an optimal one; my model therefore does not intend to identify the best
possible solution, but only to mimic the mechanisms that real agents develop. The model will
initially focus on the categorization of objects (actions), and then will be extended to
interactive games.
My model has some points in common with the model of “choice by checklist”
presented by Mandler, Manzini, and Mariotti (2008). In this paper, the authors describe a
model that exploits checklists in order to choose an object from a set. This model assumes
that the possible alternatives are all known to the agents but that the characteristics of each
object are not observed from the beginning but rather learned sequentially, following a
lexicographic rule. Specifically, the i characteristic of an object is observed only if it has been
verified that the object has the i-1 characteristic; all the objects that do not have the i-1
characteristic are eliminated. The agents choose the option that remains after this process of
sequential elimination. This model is useful when the characteristics required by agents are
binding, but it is not possible to use it when none of the characteristics is compulsory. Indeed,
according to this model, once it is verified that an object does not have a characteristic, it is
eliminated from the set of the possible choices and all the following attributes that
characterize it will never be observed. What I propose is a model where the characteristics are
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sequentially observed as in Mandler, Manzini, and Mariotti (2008), but where the number of
objects increases over time. I also assume that the elements will never be eliminated by the set
of possible choices. The elements will be grouped based on the observed characteristics and
agents’ knowledge about the categories will be more accurate for those that contain more
elements.
In the third phase, I will empirically investigate if subjects develop categories in order
to manage the strategic situations they confront.
Economists have carefully classified 2x2 games into categories (Rapoport and Guyer,
1966) and identified an optimal strategy for every category. What I expect to find is that naïve
agents are not able to distinguish games that are similar but not the same and for which
different strategies and equilibria have been identified. It seems unlikely that agents are able
to detect the differences upon a first observation, while it is plausible to expect that their
ability to identify games will increase with experience. But even if they are able to distinguish
between games, it might be that they are unable to identify new optimal strategies for
different games, and then decide to apply the strategies learned in previous situations.
From this perspective, there are two possible ways of identifying categories: the first is
to define category as a group of different games among which an agent is unable to
distinguish, so that the games are the same from the agent’s point of view even if economists
have identified them as different; the second is to define as a category a group of games for
which an agent apply the same strategy even if the agent knows that the games are different.
In order to explore whether agents are able to distinguish between different types of
games and whether they transfer the strategies between games, I will run a series of
experiments. As for the experiments in phase one, I will run them by grouping each player in
pairs with an unknown partner that will be randomly changed at every round. One way to
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analyze how subjects categorize is to let them practice with some games and then to make
them play some other games that appear similar, but have different equilibria, or games that
do not appear similar, but that actually have the same equilibria. In this way it may be
possible to investigate categorization directly from agents’ choices; otherwise another option
is to let them familiarize themselves with some games and then to introduce a questionnaire.
These experiments will also allow me to test the model developed in the second phase.
All the proposed experiments will be run at the Computable Experimental Economic
Laboratory (CEEL, University of Trento), with funding that hopefully will come from a PRIN
project on “Categorization”.
Conclusions
Since Pareto’s reformulation of choice theory, economics was conceived as a fully rational
science, leaving no space for human feelings (Bruni and Sugden, 2007). People were
supposed to be infallible agents, more similar to machines rather than to real subjects. If those
assumptions are plausible for macroeconomic dynamics where the behavior of the individual
is irrelevant, they are less plausible when individual decision making is analyzed. For these
reasons, new fields of research have grown in recent years focusing on human behavior and
psychology. Experiments have provided evidence of the bounded rationality of agents both in
individual and in interactive strategic situations. The aim of my thesis is to investigate the role
that different types of mental representations have in the choice process, by focusing mainly
on categorization and mental models in interactive games.
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References
Allais, M. (1953). Le Comportement de l'Homme Rationnel Devant le Risque: Critique des
Postulats et Axiomes de l'Ecole Americane. Econometrica, 21(4), 503-546.
Bruni, L., & Sugden, R. (2007). The Road Not Taken: How Psychology Was Removed From
Economics, and How It Might Be Brought Back. Economic Journal, 117(516 (1)),
146-173.
Camerer , C. F. (2003). Behavioral Game Theory: Experiments in Strategic Interaction.
Princeton: Princeton University Press.
Cooper, D. J., & Van Huyck, J. B. (2003). Evidence on the Equivalence of the Strategic and
Extensive Form Representation of Games. Journal of Economic Theory, 110(2), 290308.
Devetag, G. (2005). Precedent Transfer in Coordination Games: An Experiment. Economic
Letters, 89(2), 227-232.
Devetag, G., & Warglien, M. (2008). Playing the Wrong Game: An Experimental Analysis of
Relational Complexity and Strategic Misrepresentation. Games and Economic
Behavior, 62(2), 364-382.
Fehr, E., & Schmidt, K. M. (1999). A Theory Of Fairness, Competition, And Cooperation.
Quarterly Journal of Economics, 114(3), 817-868.
Fryer, R., & Jackson, M. O. (2008). A Categorical Model of Cognition and Biased Decision
Making. B.E. Journal of Theoretical Economics, 8(1), 1-42.
Güth, W., Schmittberger, R., & Schwarze, B. (1982). An Experimental Analysis of
Ultimatum Bargaining. Journal of Economic Behavior and Organization, 3(4), 367388.
Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. R. (1986). Induction: Process of
inference, Learning, and Discovery. London, England: The MIT Press.
Kagel, J. H., & Roth, A. E. (1995). The Handbook of Experimental Economics. Princeton:
Princeton University Press.
Knez, M., & Camerer, C. (2000). Increasing Cooperation in Prisoner's Dilemmas by
Establishing a Precedent of Efficiency in Coordination Games. Organizational
Behavior and Human Decision Processes, 82(2), 194-216.
Kreps, D. M. (1990). Game Theory and Economic Modelling. New York: Oxford University
Press.
Leland, J. W. (1994). Generalized Similarity Judgments: An Alternative Explanation for
19
Choice Anomalies. Journal of Risk and Uncertainty, 9(2), 151-172.
Leland, J. W. (1998). Similarity Judgments in Choice under Uncertainty: A Reinterpretation
of the Predictions of Regret Theory. Management Science, 44(5), 659-672.
Leland, J. W. (2001). Similarity Uncertainty, and Time-Tversky (1969) Revisited. IBM
Research Report, n. RC22120 (99107).
Leland, J. W. (2002). Similarity Judgments and Anomalies in Intertemporal Choice.
Economic Inquiry, 40(4), 574-581.
Leland, J. W. (2006). Equilibrium Selection, Similarity Judgments and the "Nothing to
Gain/Nothing to Lose" Effect. CEEL Working Paper, n. 0604, Trento: University of
Trento.
Mandler, M., Manzini, P., & Mariotti, M. (2008). A Million Answers to Twenty Questions:
Choosing by Checklist. IZA Discussion Papers,n. 3377.
Manzini, P., & Mariotti, M. (2008). Categorize The Choose: Boundedly Rational Choice and
Welfare. Queen Mary Working Paper, n. 561/2006, Queen Mary University.
McKelvey, R. D., & Palfrey, T. R. (1992). An Experimental Study of the Centipede Game.
Econometrica, 60(4), 803-836.
Rabin, M. (1993). Incorporating Fairness into Game Theory and Economics. American
Economic Review, 83(5), 1281-1302.
Rapoport, A., & Guyer, M. (1966). A Taxonomy of 2X2 Games. Yearbook of the Society for
General Systems Research, XI, 203-214.
Rosch, E., Mervis, C. B., Gray, W. D., Johnson, D. M., & Boyes-Braem, P. (1976). Basic
Objects in Natural Categories. Cognitive Psychology, 8(3), 382-439.
Rubinstein, A. (1988). Similarity and Decision-Making under Risk (Is There a Utility Theory
Resolution to the Allais Paradox?). Journal of Economic Theory, 46(1), 145-153.
Schelling, T. C. (1963). The Strategy of Conflict. New York: Oxford University Press.
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