论文标题
多人进化稳定策略的计算复杂性
Computational Complexity of Multi-Player Evolutionarily Stable Strategies
论文作者
论文摘要
在本文中，我们研究了计算多游戏对称游戏中进化稳定策略（ESS）的计算复杂性。对于两人游戏，对于σ2，决定ESS的存在是完整的，这是多项式时间层次结构的第二层。我们表明，确定多玩家游戏的ESS存在与真实多项式层次结构的第二层密切相关。也就是说，我们证明了对于复杂性类来说很难，我们将其表示为\ d。 \ forall r，是\ forall r的成员，在该\ forall r中，以前的类使后者限制了存在的量化变量，而不是真实价值。作为我们结果的一种特殊情况，可以得出确定对\ forallR的确定是否完整的EST。与ESS密切相关的概念是本地优越的策略（LSS）。我们扩展了有关ESS的结果，并表明确定多人游戏的LSS的存在同样很难\ forall r和\ forall r的成员，并且作为一个特殊情况，决定给定策略是否是\ forall R. \ forall R.
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.
