🤖 AI Summary
This paper addresses the lack of a pure choice-theoretic foundation for Nash equilibrium. We propose the first axiomatic characterization framework for Nash equilibrium based solely on abstract choice functions. Our approach introduces two novel axioms—*contraction consistency* and *expansion consistency*—inspired by classical choice-theoretic principles, supplemented by two additional intuitive axioms. Together, these fully characterize the Nash equilibrium correspondence across arbitrary strategy sets (finite or infinite) and encompass both pure-strategy and mixed-strategy equilibria. Crucially, the framework dispenses with standard assumptions such as utility representation, rationalizability of preferences, or continuity, thereby delivering a genuinely choice-theoretic definition of Nash equilibrium. The resulting characterization unifies diverse game structures—including finite, infinite, and continuous games—enhancing the generality, interpretability, and formal rigor of the equilibrium concept. This work establishes a new paradigm for interdisciplinary research at the interface of game theory and decision theory.
📝 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.