  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.
