A Robust Characterization of Nash Equilibrium

We give a robust characterization of Nash equilibrium by postulating coherent behavior across varying games: Nash equilibrium is the only solution concept that satisfies consequentialism, consistency, and rationality. As a consequence, every equilibrium refinement violates at least one of these properties. We moreover show that every solution concept that approximately satisfies consequentialism, consistency, and rationality returns approximate Nash equilibria. The latter approximation can be made arbitrarily good by increasing the approximation of the axioms. This result extends to various natural subclasses of games such as two-player zero-sum games, potential games, and graphical games.