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 axiom of Independence assumed of players’ preferences. 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 Cartesian product form consideration equilibria which is nonempty and includes any Nash equilibrium, if one exists. It coincides with the set of Nash equilibria or minimax strategy tuples if preferences additionally satisfy Continuity. Further, consideration equilibria of a game are contained in the set of minimax strategy tuples of the continuous approximation of the given game.