论文标题
在平面bimatrix游戏上，计算统一的纳什均衡的NP硬度
NP-hardness of Computing Uniform Nash Equilibria on Planar Bimatrix Games
论文作者
论文摘要
我们研究了在非获胜的bimatrix游戏上计算均匀NASH平衡的复杂性。众所周知，即使Bimatrix游戏是Win-lose（Bonifaci et al。，2008），这种问题也是NP完整的。幸运的是，如果获胜的bimatrix游戏是平面的，那么统一的纳什均衡总是存在。我们有一种多项式时间算法，用于找到平面赢得bimatrix游戏的均匀NASH平衡（Addario-Berry等，2007）。剩下以下问题：在平面非获胜的bimatrix游戏上计算统一的纳什均衡程度有多难？本文解决了这个问题。我们证明，确定非获胜的平面bimatrix游戏是否具有均匀的NASH平衡的问题也是NP完整的。
We study the complexity of computing a uniform Nash equilibrium on a non-win-lose bimatrix game. It is known that such a problem is NP-complete even if a bimatrix game is win-lose (Bonifaci et al., 2008). Fortunately, if a win-lose bimatrix game is planar, then uniform Nash equilibria always exist. We have a polynomial-time algorithm for finding a uniform Nash equilibrium of a planar win-lose bimatrix game (Addario-Berry et al., 2007). The following question is left: How hard to compute a uniform Nash equilibrium on a planar non-win-lose bimatrix game? This paper resolves this issue. We prove that the problem of deciding whether a non-win-lose planar bimatrix game has uniform Nash equilibrium is also NP-complete.
