A Rational Way of Playing: Revision Theory for Strategic Interaction

Abstract

Gupta (2011) has proposed a definition of strategic rationality cast in the framework of his revision theory of truth. His analysis, relative to a class of normal form games in which all players have a strict best reply to all other players’ strategy profiles, shows that game-theoretic concepts (e.g. Nash equilibrium) have revision-theoretic counterparts. We extend Gupta’s approach to deal with normal form games in which players’ may have weak best replies. We do so by adapting intuitions relative to Nash equilibrium refinements (in particular, trembling-hand perfection and properness) to the revision-theoretic framework. We prove that there is a precise equivalence between trembling-hand perfect equilibria in two-player normal games and a revision-theoretic property. We then introduce lexicographic choice of action as a way to represent players’ expectations, which allows our analysis to reach full generality. Finally, we provide an example of the versatility of revision theory as applied to strategic interaction by formalizing a risk-and-compensation procedure of strategic choice in the revision-theoretic framework.