A Robust Characterization of Nash Equilibrium

TL;DR

This paper provides a unique axiomatic characterization of Nash equilibrium, showing it as the only solution concept satisfying specific behavioral axioms across varying games, and discusses implications for equilibrium refinements.

Contribution

It introduces a set of axioms that uniquely characterize Nash equilibrium and demonstrates that other solution concepts violate these axioms or only approximate Nash equilibria.

Findings

Nash equilibrium is the only solution satisfying the axioms.

Equilibrium refinements violate at least one of the axioms.

Approximate solutions satisfy the axioms in certain subclasses of games.

Abstract

We characterize Nash equilibrium by postulating coherent behavior across varying games. Nash equilibrium is the only solution concept that satisfies the following axioms: (i) strictly dominant actions are played with positive probability, (ii) if a strategy profile is played in two games, it is also played in every convex combination of these games, and (iii) players can shift probability arbitrarily between two indistinguishable actions, and deleting one of these actions has no effect. Our theorem implies that every equilibrium refinement violates at least one of these axioms. Moreover, every solution concept that approximately satisfies these axioms returns approximate Nash equilibria, even in natural subclasses of games, such as two-player zero-sum games, potential games, and graphical games.