多人进化稳定策略的计算复杂性
Computational Complexity of Multi-Player Evolutionarily Stable Strategies
摘要：
本文研究了多人对称博弈中计算进化稳定策略的计算复杂性。对于两人博弈，判定ESS的存在对于多项式时间层次结构的第二层即ε 2是完全的。我们发现，决定存在的ESS的多人游戏是密切相关的第二个层次的真正的多项式时间层次。也就是说，我们表明，这个问题是困难的复杂性类，我们表示为\exists D。\forall R，并且是\exists \forall R的成员，其中前一个类通过使存在量化变量是布尔值而不是实值来限制后者。作为我们结果的一个特例，我们得出结论：对于\forall R，判定一个给定的策略是否是ESS是完全的.与ESS密切相关的一个概念是局部优越策略（LSS）。我们推广了ESS的结果，证明了对于\exists D \forall R和\exists \forall R的成员，判定多人博弈的LSS的存在性同样困难，并且作为特例，判定给定策略是否是LSS对于\forall R是完全的.
英文摘要：
In this paper we study the computational complexity of computing an evolutionary stable strategy (ESS) in multi-player symmetric games. For two-player games, deciding existence of an ESS is complete for Σ 2 , the second level of the polynomial time hierarchy. We show that deciding existence of an ESS of a multi-player game is closely connected to the second level of the real polynomial time hierarchy. Namely, we show that the problem is hard for a complexity class we denote as \exists D . \forall R and is a member of \exists\forall R, where the former class restrict the latter by having the existentially quantified variables be Boolean rather then real-valued. As a special case of our results it follows that deciding whether a given strategy is an ESS is complete for \forall R. A concept strongly related to ESS is that of a locally superior strategy (LSS). We extend our results about ESS and show that deciding existence of an LSS of a multiplayer game is likewise hard for \exists D \forall R and a member of \exists\forall R, and as a special case that deciding whether a given strategy is an LSS is complete for \forall R.
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