Two-person zero-sum games without expected utility preferences: a proposal

Abstract

A solution concept for two-person zero-sum games is proposed with only the Independence axiom assumed of players' preferences. We do not assume Continuity which is critical for many fixed-point theorems. Each player is shown to admit a set of "admissible" strategies assuring minimum guarantees. Rationality requires agents to reject non-admissible strategies in further considerations. Knowledge assumptions imply iterated elimination of non-admissible strategies resulting in surviving sets whose cross product are "consideration equilibria". Consideration equilibria always exist and include Nash equilibria if any. Consideration equilibria and Nash equilibria (or, minimax strategies) coincide if preferences are also Continuous. Further, consideration equilibria of a game are contained in the set of minimax strategies of the continuous approximation of the given game. Three applications of the solution concept are presented.