A choice-based axiomatization of Nash equilibrium
Michele Crescenzi
TL;DR
This paper provides a complete axiomatization of Nash equilibrium for normal-form games by four axioms—Independence of Irrelevant Strategies, Merging Consistency, Invariance to Strictly Dominated Strategies, and Joint Optimality—valid across pure and mixed strategies and without requiring utility representations. It proves that, on d-closed classes of games, these axioms characterize the Nash equilibrium correspondence exactly, and it discusses logical independence, one-player special cases, domain constraints, and how the framework relates to established axioms like CONS, CIIS, and COCONS. The work extends the axiomatic analysis of Nash equilibria to broader game classes and provides insights into the minimal rationality requirements for equilibrium selection. It also clarifies how domain properties affect the applicability of the axiomatization and situates the results within the broader literature on choice-theoretic consistency for strategic interactions.
Abstract
An axiomatic characterization of Nash equilibrium is provided for games in normal form. The Nash equilibrium correspondence is shown to be fully characterized by four simple and intuitive axioms, two of which are inspired by contraction and expansion consistency properties from the literature on abstract choice theory. The axiomatization applies to Nash equilibria in pure and mixed strategies alike, to games with strategy sets of any cardinality, and it does not require that players' preferences have a utility or expected utility representation.