A game is solvable if the set of Nash equilibria is nonempty and interchangeable. A pairwise solvable game is a two-person symmetric game in which any restricted game generated by a pair of strategies is solvable. We show that the set of equilibria in a pairwise solvable game is interchangeable. Under a quasiconcavity condition, we derive a complete order-theoretic characterization and some topological sufficient conditions for the existence of equilibria, and show that if the game is finite, then an iterated elimination of weakly dominated strategies leads precisely to the set of Nash equilibria, which means that such a game is both solvable and dominance solvable. All results are applicable to symmetric contests, such as the rent-seeking game and the rank-order tournament, which are shown to be pairwise solvable. Some applications to evolutionary equilibria are also given.

中文翻译：

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两人成对可解博弈

如果纳什均衡集非空且可互换，则博弈是可解的。成对可解博弈是一种两人对称博弈，其中由一对策略生成的任何受限博弈都是可解的。我们证明了成对可解博弈中的均衡集是可互换的。在准空性条件下，我们推导出了一个完整的序论表征和均衡存在的一些拓扑充分条件，并证明如果博弈是有限的，那么弱支配策略的迭代消除恰好导致纳什均衡集，这意味着这样的博弈既是可解的，又是支配性的可解的。所有结果都适用于对称竞赛，例如寻租游戏和排名比赛，它们被证明是成对可解的。