A choice-based axiomatization of Nash equilibrium

TL;DR

This paper provides an axiomatic characterization of Nash equilibrium in normal form games, using four intuitive axioms that apply to pure and mixed strategies without utility assumptions.

Contribution

It introduces a new axiomatic framework that fully characterizes Nash equilibrium, inspired by choice theory, applicable to all strategy set sizes and strategy types.

Findings

Nash equilibrium is characterized by four simple axioms.

The axiomatization applies to pure and mixed strategies.

No utility or expected utility representation is required.

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.