Internal Game Theory

Tassos Patokos

• Publisher: Routledge
• Year: 2013
• eBook ISBN: 9781135933364
• Topic: Economics
• Subtopic: Economic Theory
• Index: Economics

Traditional game theory requires at least two individuals. This book extends game theory to the inner workings of a single person.

Using game theory to analyse single individuals makes sense if one thinks of individuals as consisting of two or more relatively autonomous partitions that might have conflicting motives. This is not to say that individuals are literally made up from multiple selves; it only suffices that we adopt a portrayal of the individual as a multilayered entity or of a dual nature, in a manner similar to Adam Smith's depiction of an "impartial spectator" existing within the individual,

The notion that individuals may be considered as collections of distinct partitions or "sub-selves" has been challenging writers from diverse fields for many centuries. This book breaks new ground in combining psychological with evolutionary game theory, making for a highly promising way towards a better understanding of the individual and the development of their behaviour, along with the individual's own perceptions on it.

1 Overview

1.1 Inner conflicts and individual choice theory

Individuals are fraught with inner conflicts. Self-doubt, self-control, even the loathing of one's self is the stuff of life. Ever since Sigmund Freud discovered the subconscious and depicted the human condition as a field on which different sub-intentional agencies tussle for control of the conscious mind (which does the decision making), our psychology has emerged as a central player in the evolution of human thought, society, and even economy. John Maynard Keynes' evocation of animal spirits in the 1930s (see Keynes 1936, but also the book by Akerlof and Shiller 2009), in the context of explaining the penchant of capitalist economies toward crises, has established the importance of the games within our minds regarding the shape of our external social world. In this context, there seems to be something amiss in the manner in which game theory, despite the lofty status it seems to have acquired for itself over the past decades, neglects the inner conflicts and games that typify our demeanour and determine our actions. This book is about proposing one way in which this theoretical lacuna can be remedied.

Inner conflicts emerge even at a trivial level of everyday activity, as happens, for example, when someone tries to lose weight but somehow cannot refrain from overeating, or promises to not spend more than a certain amount when out shopping, but ends up in a spending spree. Most individuals are aware of these con-flicts, and it is not unusual for them to devise plans in order to eschew this kind of unpleasant situations: impulsive eaters sometimes try to consciously visit the supermarket when they are not hungry, in an attempt to stock less food at home and hence make it impossible to eat more than they would like; similarly, people who are inclined to spend too much are known to often go shopping carrying a limited amount of cash and no credit or debit cards, making themselves physically incapable of spending more than what they have resolved to spend. One could think of countless scenarios like these: a gambler who willingly orders a casino's security personnel to prevent them from entering the premises again, or a smoker who chooses to not buy cigarettes while the tobacco store is still open. They are rather common occurrences of an internal clash of preferences, which some individuals drastically try to circumvent by imposing constraints to themselves. One of the most celebrated examples is Ulysses tying himself to the mast of his ship before reaching the land of the Sirens: since Ulysses knew that succumbing to the temptation of their singing would be fatal, he protected himself against what he knew would be an unbeatable — and deadly — urge to follow the Sirens once he heard their song.

In all these examples, it is as if there are multiple entities within a single individual, whose interests are not aligned. The smoker wants to get rid of the unhealthy habit, but a part of him or her keeps resisting. Ulysses wants to hear the Sirens singing, but then again, he does not trust himself to do what is in his best interest once the song begins. The idea that an individual may be considered as made up of several partitions can be found in texts as early as Plato's Republic, where ‘divisions of the soul’ are believed to be the source of inner conflicts. The notion of a possible ‘multiplicity’ of the self has been studied by countless researchers from diverse fields such as philosophy, psychology, the medical sciences or economics. The most well-known view is perhaps that of Freud, who maintained that individuals are comprised of an ‘id’, an ‘ego’ and a ‘superego’ which interact with each other. The Freudian superego, some kind of ‘inner judge’ that operates in our psychic structure, is reminiscent of the ‘impartial spectator’ that Adam Smith described in his Theory of Moral Sentiments ([1759] 2002), an internal effort to view ourselves with the (objective) eyes of other people. Metaphorically, one might as well regard the impartial spectator as a second person living in our bosom, passing judgement on our preferences and actions.

Some theorists would perhaps be quick to regard the concept of multiple selves within an individual as a special, pathological case, indicative of some sort of schizophrenia (or some milder predicament, but out of the ordinary nonetheless). If this was indeed true, then study of these cases would be of limited interest, at least from the perspective of economics, whose individual choice theory practically ignores individual profiles that deviate from the rational agent standard. In economics, individual rationality means that the agents' preferences must have certain properties, one of which is referred to as ‘completeness’. Completeness means that the individual should always know what they prefer over any two alternatives; they might be indifferent between two options, but they are not allowed ignorance on what they prefer. Rational agents are also assumed to try and reach whatever is at the top of their preference lists.

Economists' definition of rationality seems to be at odds with the smoker who would rather not smoke but actually does, or the person who wants to lose weight but cannot help overeating. In fact, one could theoretically argue that such cases do not meet the definition of rationality, and unsurprisingly so: smoking is, after all, an addiction, and failing to stick to a diet could be classified as an eating disorder; hence it would seem that, rather, this is territory for medical research, as opposed to being material falling under a general theory of individual choice that is supposed to be preoccupied with normal (non-pathological) cases. Allowing for multiple selves with conflicting preferences to coexist within a single individual would expectedly undermine the requirement for completeness of preferences (and hence, rationality) — lest we forget that a

Box 1.1 Arrow's impossibility theorem

Arrow's impossibility theorem (Arrow 1951) is one of the most important results of public choice theory. Without going into the technicalities, Arrow's theorem says — in a nutshell — that individual preferences cannot translate to collective preferences. More specifically, if we have a group consisting of N individuals, each one of whom has certain preferences, then we cannot use the preferences of these individuals to construct a preference list for all of them as a group — unless we accept one of those N individuals to be a ‘dictator’ (i.e. someone whose individual preferences will always coincide with the collective preferences).

Arrow's impossibility theorem is a quite startling theoretical result. In essence, it means that it makes little sense to speak of the ‘common good’ or of ‘common interests’ within a group, because these notions cannot even be defined. In the context of our discussion, if we accept that the self is divided into sub-selves that don't necessarily have the same preferences, then Arrow's theorem says that we simply cannot arrive at pinning down the preferences of the self as a unified whole by trying to synthesise the preferences of the different sub-selves.

synthesis of these preferences would be infeasible courtesy of Arrow's impossibility theorem (see Box 1.1).

Nevertheless, to regard the notion of partitioned individuals as a special case undeserving of economists' attention would mean the exclusion of most of the population from the theory's ambit. A theory that only deals with fully integrated, undivided, consistent individuals would lose its claim to be a positive theory of real-world individuals and might end up as too ambitious a portrayal of some ‘ideal’ type. Although individuals with perfectly clear preference orderings might conceivably exist, common sense indicates that they would be the exception rather than the norm; conflicting preferences are likely to appear in almost any person at some stage of their lives, and this is why terms such as self-knowledge, self-perception, self-consciousness or self-deception are part of our vocabulary (and not just terms used by medical experts). These words would have little meaning if the person was conceived as a compact unity with well-defined interests, motivations and desires.

One could argue that the emergence of inner conflicts does not necessarily mean that individuals are divided into multiple selves. As Elster (1986, pp. 30–31) notes, someone's cognitive coordination problems or motivational conflicts ‘do not sort themselves out in an inner arena where several homunculi struggle to get the upper hand’. Arguments like this are not incompatible with acknowledging that most people have frequent ethical dilemmas, attempt to ‘manage themselves’, or try to come to terms with the ‘impartial spectator’ in them. To put it differently, whether inner conflicts happen within an omniscient, unified self or within a collection of distinct selves that form the individual is ultimately not too important, if one recognises the possibility of clashing preferences; this is an observation that, at least, implies some greater complexity of the individual than what is seen in the standard take of economics. Multiple selves or not, it is hard to disagree with a however abstract model for the human agent where different personality aspects of the same person are in antagonistic terms.

To be sure, numerous economists have elaborated on the issue over the past decades. One among the first to have done so is Nobel laureate Thomas Schelling, who coined the term ‘egonomics', and who provided several relevant examples, arguing that ‘in these examples, everybody behaves like two people’ (Schelling 1978, p. 290). For examples of more recent research, Prelec and Bodner (2003) make reference to self-signalling, while Fudenberg and Levine (2006) speak of a ‘dual self’, and, in an attempt to explain time inconsistencies in individual behaviour, view one-actor decision problems as a game between a sequence of short-run impulsive selves and a long-run patient self (we will delve into some of these examples in Chapter 5). The fact that the majority of the authors who have dealt with these ideas have done research in game theory is telling: if an individual is assumed to be a multi-layered entity, then game theoretical tools appear to be more apt to study the economic agent than individual choice theory.

One probable reason why the use of game theory in individual choice settings is rather rare is that individual choice theory does not need to proclaim individuals with conflicting preferences as irrational; it can very well study them by use of its own existing methodology. According to the supporters of mainstream economic theory, multiple selves would not really threaten completeness of preferences, because, after all, the individual will have to ultimately choose something. The smoker, a bit clueless as to how to rank his or her desire for another cigarette against his or her will to fight the addiction, would perhaps not be able to write down his or her preference list for us, but from the moment (s)he chooses to have (or not have) another cigarette, we eventually know that, actually, the preference for (not) smoking was stronger. This is, of course, a ‘revealed preference’ argument: in a sense, we may recover individual preferences by observing the choices that the individuals make. Now, as we will see in the next chapter, if these choices satisfy a seemingly innocuous consistency criterion (known as ‘the strong axiom of revealed preference’), it can be proved that the underlying preferences must be rational. In other words, even if the definition of rationality that imposes restrictions on the agents' preferences is not practical when it comes to dealing with inner conflicts, the (equivalent) choice-based approach to rationality does not face such problems, since it can only be applied once an actual choice has been made (and hence, the conflict has been resolved).

The issue, however, is not whether the strong axiom of revealed preference is a plausible consistency criterion or not. Even if most theorists agreed that it is, using it would tell us nothing about the cognitive or behavioural processes that lead to a particular choice. In this regard, an avid smoker would appear to have the same (revealed) preferences as someone who struggles to quit smoking but is unable to. Maybe this abstraction would make sense for a number of research purposes, but if the matter under study is inner imbalance, motivational turmoil and conflicting preferences, then a theory essentially asking us to wait up until the agent makes a decision and then infer their preferences from what they chose would be simply insufficient and inadequate.

It seems that individual choice theory can neither ignore inner conflicts (on the grounds that they allegedly correspond to pathological — irrational — cases), nor can it proclaim them a posteriori resolved (and as such, not very interesting for further study) — at least not without loss of too much detail. Losing these details would perhaps not matter if the task at hand was to study something trivial such as the demand for apples or oranges (in what would be a textbook-like exercise), but it would be important if the study went beyond mere choice and also dealt with the individual's psyche and the individual's internal processes and reasons for acting.

1.2 Partitioned individuals and game theory

Once we decide to venture into a theoretical world of multi-layered individuals and accept the presence of distinct entities within the person, each of which possesses potentially different preferences and separate beliefs, game theory seems to offer convenient tools for taking our inquiry further. Game theory, of course, and as we will explain in Chapter 4, is not without its own theoretical problems. Because it adopts and builds on the individual rationality framework, it is often argued that game theory inherits all the problems of individual choice theory, and then adds some more of its own, due to the additional assumptions of common knowledge of rationality and of the consistency of beliefs needed to obtain a Nash equilibrium (the main theoretical concept of game theory). Even with these quite restricting assumptions, most games have multiple Nash equilibria, which means indeterminacy in both the prescriptive and the predictive aspects of the theory.

Ironically enough, the criticism that game theory relies on an unrealistic account of individual rationality seems to be (at least, partly) addressed if this very same rationality concept is used separately for multiple partitions of the same individual. A theorist who finds that one preference ordering cannot possibly suffice for describing a person, would perhaps agree that simultaneous use of multiple preference orderings would be a better modelling option, if only for addressing the usual objection that individual choice theory portrays agents as inappropriately one-dimensional. If, however, the individual is thought of as a collection of distinct selves, it is no longer one-dimensional to assume individual rationality for each one of these selves, since these selves are just components of a larger entity, and not autonomous, standalone agents.

The assumption of common knowledge of rationality is trickier in this context, and it comes down to whether one would be justified to assume that there is common knowledge of rationality among the different partitions that an individual is made up of. A quick answer would be an emphatic yes; after all, since game theorists get away with assuming common knowledge of rationality among strangers, it would be odd to not assume it for singular divisions of the same person. The part of the smoker who enjoys cigarettes and the part of them who wants to quit smoking both try to maximise their utility and this could be assumed to be common knowledge, in the sense that the individual is fully conscious of the conflict in him or her, and can perfectly reason from the point of view of both sides. On second thoughts, however, intrapersonal common knowledge of rationality would exclude some instances of self-deceit and hence should not be taken for granted. For a rough example, the self wishing to smoke might not operate on the assumption that the self wanting to quit is rational (i.e. really wants to quit), in which case the conflict is minimal: the person is just deluding themselves with some wishful thinking, and it is not too much of a struggle before they light up again.

Self-deception unavoidably raises the issue of rational beliefs. Of all the assumptions of game theory, the assumption that the players' beliefs are consistently aligned (this assumption will be properly explained in Chapter 4) is the one that has been criticised the most, on the grounds that it is not very realistic, and that it practically implies some sort of ‘telepathy’ between the players. While this is a sound argument, it nevertheless has to be remembered that game theorists look for equilibria (as opposed to solutions), and it would clearly be inapt to accept equilibria where the players' beliefs would not be accurate; this would mean that at least one of the players would not have given their best reply to the other players' strategies, which would defy the concept of an equilibrium in the first place. That said, even if consistent alignment of beliefs is fine as a purely theoretical requirement, it seems that, with regards to plausibility, it is an assumption that asks too much of the players. Does it remain a problematic assumption if we take it to the single player and assume intrapersonal consistent beliefs? This is one of the questions that lie at the heart of this book.

For one thing, the term ‘intrapersonal beliefs’ presupposes some kind of multiplicity of the self (or, at least, a duality), the minimum division being between the person who acts and a belief system that reflects on these actions. Perhaps this seems a too fictitious depiction of the individual, but there are numerous commonly used words that, more or less, describe the same thing — such as self-esteem, self-concept or self-perception. Someone who thinks of themselves as a kind person holds a belief in his or her kindness which might or might not be accurate. Someone might have an impressively high self-esteem in attracting people of the opposite sex, even when the latter find them repulsive. Intrapersonal beliefs are im...

Table of contents

• Cover
• Half Title
• Routledge Advances in Game Theory
• Title Page
• Copyright Page
• Table of Contents
• List of illustrations
• Foreword
• Acknowledgements
• 1 Overview
• 2 Individual behaviour
• 3 The partitioned self
• 4 A critical overview of game theory
• 5 The importance of intrapersonal beliefs: psychological game theory and internal games
• 6 Internal games and historical time
• 7 Internal game theory: an assessment
• References
• Index