# The Bounds of Reason: Game Theory and the Unification of the Behavioral Sciences

Herbert Gintis
Pages: 304
https://www.jstor.org/stable/j.ctt7s97x

1. Front Matter
(pp. i-vi)
(pp. vii-xii)
3. Preface
(pp. xiii-xviii)
4. 1 Decision Theory and Human Behaviour
(pp. 1-29)

Decision theory is the analysis of the behavior of an individual facing nonstrategic uncertainty—that is, uncertainty that is due to what we term “Nature”(a stochastic natural event such as a coin flip, seasonal crop loss, personal illness, and the like) or, if other individuals are involved, their behavior is treated as a statistical distribution known to the decision maker. Decision theory depends on probability theory, which was developed in the seventeenth and eighteenth centuries by such notables as Blaise Pascal, Daniel Bernoulli, and Thomas Bayes.

Arational actoris an individual withconsistent preferences(§1.1). A rational actor need...

5. 2 Game Theory: Basic Concepts
(pp. 30-44)

Anextensive form game${\cal G}$consists of a number ofplayers, agame tree, and a set ofpayoffs. A game tree consists of a number ofnodesconnected bybranches. Each branch connects ahead nodeto a distincttail node. Ifbis a branch of the game tree, we denote the head node ofbbybh, and the tail node ofbby${b^h}$.

Apathfrom nodeato node${a'}$in the game tree is a connected sequence of branches starting ataand ending at${a'}$.¹ If there is a path from node...

6. 3 Game Theory and Human Behaviour
(pp. 45-82)

Game theory is multiplayer decision theory where the choices of each player affect the payoffs to other players, and the players take this into account in their choice behavior. In this chapter we address the contribution of game theory to the design of experiments aimed at understanding the behavior of individuals engaged in strategic interaction. We call thidbehavioural game theory.

Game theory is a general lexicon that applies to all life forms. Strategic interaction neatly separates living from nonliving entities and defines life itself. Strategic interaction is the sole concept commonly used in the analysis of living systems that...

7. 4 Rationaliability and Common Knowledge of Rationality
(pp. 83-101)

To determine what a rational player will do in a game, eliminate strategies that violate the cannons of rationality. Whatever is left we callrationalizable. We show that rationalizability in normal form games is equivalent to the iterated elimination of strongly dominated strategies, and the epistemological justification of rationalizability depends on thecommon knowledge of rationality(Tan and Werlang 1988).

If there is only one rationalizable strategy profile, it must be a Nash equilibrium, and it must be the choice of rational players, provided there is common knowledge of rationality.

There is no plausible set of epistemic conditions that imply...

8. 5 Extensive From Rationalizability
(pp. 102-120)

The extensive form of a game is informationally richer than the normal form since players gather information that allows them to update their subjective priors as the game progresses. For this reason, the study of rationalizability in extensive form games is more complex than the corresponding study in normal form games. There are two ways to use the added information to eliminate strategies that would not be chosen by a rational agent: backward induction and forward induction. The latter is relatively exotic (although more defensible) and will be addressed in chapter 9. Backward induction, by far the most popular technique,...

9. 6 The Mixing Problem: Purification and Conjectures
(pp. 121-131)

Economic theory stresses that a proposed mechanism for solving a coordination problem assuming self-regarding agents is plausible only if it

isincentive compatible: each agent should find it in his interest to behave as required by the mechanism. However, a strictly mixed-strategy Nash equilibrium$\sigma * = (\sigma _1^*, \ldots ,\sigma _n^*)$fails to be incentive compatible, because a self-regarding agentiis indifferent to any mixed strategy in the support of$\sigma _i^*$. This chapter deals with the solution to this problem. We conclude that, while ingenious justifications of the incentive compatibility of mixedstrategy Nash equilibria have been offered, they fail except in a large majority of...

10. 7 Bayesian Rationality and Social Epistemology
(pp. 132-145)

At least since Schelling (1960) and Lewis (1969), game theorists have interpreted social norms as Nash equilibria. More recent contributions based upon the idea of social norms as selecting among Nash equilibria include Sugden (1986), Elster (19891, b), Binmore (2005), and Bicchieri (2006). There are two problems with this approach. The first is that the conditions under which rational individuals play a Nash equilibrium are extremely demanding (theorem §8.4), and are not guaranteed to hold simply because there is a social norm specifying a particular Nash equilibrium. Second, the most important and obvious social norms do not specify Nash equilibria...

11. 8 Common Knowledge and Nash Equilibrium
(pp. 146-163)

This chapter applies the modal logic of knowledge developed in §4.1 and §5.10 to explore sufficient conditions for a Nash equilibrium in two-player games (§8.1). We then expand the modal logic of knowledge to multiple agents and prove a remarkable theorem, due to Aumann (1976), that asserts that an event that is self-evident for each member of a group is common knowledge (§8.3).

This theorem is surprising because it appears to prove that individuals know the content of the minds of others with no explicit epistemological assumptions. We show in §8.4 that this theoremis the result of implicit epistemological assumptions...

12. 9 Reflective Reason and Equilibrium Refinements
(pp. 164-180)

In previous chapters, we have stressed the need for a social epistemology to account for the behavior of rational agents in complex social interactions. However, there are many relatively simple interactions in which we can use some form of reflective reason to infer how individuals will play. Since reflective reason is open to the players as well as to us, in such cases we expect Nash equilibria to result from play. However, in many cases there are a plethora of Nash equilibria, only some of which will be played by reasonable agents.

ANash equilibrium refinementof an extensive form...

13. 10 The Analytics of Human Sociality
(pp. 181-200)

It is often said that sociology deals with cooperation and economics deals with competition. Game theory, however, shows that cooperation and competition are neither distinct nor antithetical. Cooperation involves aligning the beliefs and incentives of agents with distinct interests, competition among groups requires cooperation within these groups, and competition among individuals may be mutually beneficial.

A major goal of economic theory is to show the plausibility of wide-scale cooperation among self-regarding individuals. In an earlier period, this endeavor centered on the Walrasian model of general market equilibrium, culminating in the celebrated fundamental theorem of welfare economics (Arrow and Debreu 1954;...

14. 11 The Evolution of Property Rights
(pp. 201-220)

This chapter illustrates the synergy among the rational actor model, game theory, the socio-psychological theory of norms and gene-culture coevolution (§7.10), highlighting the gains that are possible when ossified disciplinary boundaries are shattered. The true power of game-theoretic analysis becomes manifest only when we cast our theoretical net beyond the strictures of methodological individualism (§8.8). The underlying model is taken from Gintis (2007b). A general case for the methodological approach followed in this chapter is presented in chapter 12.

Authors tracing back to the origins of political liberalism have treated property rights as a social norm the value of which...

15. 12 The Unification of the Behavioral Sciences
(pp. 221-247)

The behavioral sciences include economics, anthropology, sociology, psychology, and political science, as well as biology in so far as it deals animal and human behavior. These disciplines have distinct research foci, but they include four conflicting models of decision making and strategic interaction, as determined by what is taught in the graduate curriculum and what is accepted in journal articles without reviewer objection. The four are the psychological, the sociological, the biological, and the economic.

These four models are not only different, which is to be expected given their distinct explanatory aims, but are alsoincompatible. That is, each makes...

16. 13 Summary
(pp. 248-249)

In a long book with many equations, it is easy to become mired in details and hence miss the big picture. This chapter is a summary book’s of the main points.

Game theory is an indispensable tool in modeling human behaviour. Behavioral disciplines that reject or peripheralize game theory are theoretically handicapped.

The traditional equilibrium concept in game theory, the Nash equilibrium is implemented by rational actors only if they share as to how the game will be played.

The rational actor model includes no principles entailing the communality of beliefs across individuals. For this reason, the complex Nash equilibria...

17. 14 Table of Symbols
(pp. 250-252)
18. References
(pp. 253-282)
19. Index
(pp. 283-286)