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

By Herbert Gintis | Go to book overview

9
Reflective Reason and Equilibrium Refinements

If we allow that human life can be governed by reason, the possibil-
ity of life is annihilated.

Leo Tolstoy

If one weight is twice another, it will take half as long to fall over a
given distance.

Aristotle, On the Heavens

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.

A Nash equilibrium refinement of an extensive form game is a criterion that applies to all Nash equilibria that are deemed reasonable but fails to apply to other Nash equilibria that are deemed unreasonable, based on our informal understanding of how rational individuals might play the game. A voluminous literature has developed in search of an adequate equilibrium refinement criterion. A number of criteria have been proposed, including subgame perfect, perfect, perfect Bayesian, sequential, and proper equilibrium (Harsanyi 1967; Myerson 1978; Selten 1980; Kreps and Wilson 1982; Kohlberg and Mertens 1986), which introduce player error, model beliefs off the path of play, and investigate the limiting behavior of perturbed systems as deviations from equilibrium play go to zero.1

I present a new refinement criterion that better captures our intuitions and elucidates the criteria we use implicitly to judge a Nash equilibrium as reasonable or unreasonable. The criterion does not depend on counterfactual

1 Distinct categories of equilibrium refinement for normal-form games, not addressed
in this chapter, are focal point (Schelling 1960; Binmore and Samuelson 2006), and risk
dominance (Harsanyi and Selten 1988) criteria. The perfection and sequential criteria are
virtually coextensive (Blume and Zame 1994) and extend the subgame perfection criterion.

-164-

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

Table of contents

  • Title Page iii
  • Contents vii
  • Preface xiii
  • 1: Decision Theory and Human Behavior 1
  • 2: Game Theory: Basic Concepts 30
  • 3: Game Theory and Human Behavior 45
  • 4: Rationalizability and Common Knowledge of Rationality 83
  • 5: Extensive Form Rationalizability 102
  • 6: The Mixing Problem 121
  • 7: Bayesian Rationality and Social Epistemology 132
  • 8: Common Knowledge and Nash Equilibrium 146
  • 9: Reflective Reason and Equilibrium Refinements 164
  • 10: The Analytics of Human Sociality 181
  • 11: The Evolution of Property Rights 201
  • 12: The Unification of the Behavioral Sciences 221
  • 13: Summary 248
  • 14: Table of Symbols 250
  • Symbols for Chapter 11 251
  • References 253
  • Index 283
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