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.

翻译：我们通过假设不同博弈中行为的一致性来刻画纳什均衡。纳什均衡是唯一满足以下公理的解概念：(i) 严格占优策略以正概率被采用，(ii) 若某个策略组合在两个博弈中均被采用，则在该两个博弈的所有凸组合中该策略组合亦被采用，(iii) 参与者可在两个不可区分的行动之间任意转移概率，且删除其中一个行动不会产生影响。我们的定理意味着任何均衡精炼都至少违反其中一条公理。此外，任何近似满足这些公理的解概念都会返回近似纳什均衡，即使在自然的博弈子类中也是如此，例如双人零和博弈、势博弈以及图博弈。