An axiomatic analysis of the Nash equilibrium concept

The purpose of this paper is to analyze axiomatically the Nash equilibrium concept. The class of games under study is a (relatively large) subclass of n-person normal form games. Solutions are correspondences which associate to each game a non empty set of strategy vectors of this game. It is shown that if a solution satisfies the axioms Independence of irrelevant alternatives (IIA) and Individual rationality (IR), then all the strategy vectors in this solution are Nash equilibria. This result holds good also if IR is replaced by Strong individual monotonicity (SIM) or Weak principle of fair compromise (WPFC).