纳什均衡的稳健刻画
A Robust Characterization of Nash Equilibrium
AI总结：
本文通过三条跨博弈一致性公理唯一刻画纳什均衡，并证明任何均衡精炼必违反至少一条公理，且近似满足公理的解概念在两人零和博弈、势博弈和图博弈等子类中仍返回近似纳什均衡。
摘要：
我们通过假设在不同博弈中行为具有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）严格占优行动以正概率被选择；（ii）若某个策略组合在两个博弈中被采用，则它也在这些博弈的任意凸组合中被采用；（iii）参与者可以在两个不可区分的行动之间任意转移概率，并且删除其中一个行动不会产生任何影响。我们的定理表明，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，例如两人零和博弈、势博弈和图博弈。
英文摘要：
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.
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