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.

翻译：我们研究了在非双赢的双马基游戏上计算统一的纳什平衡的复杂性。已知这样一个问题即使双马基游戏是双赢的,也是NP的完成(Bonifaci等人,2008年)。幸运的是,如果双马基游戏是双马基游戏,那么统一的纳什平衡就一直存在。我们有一个多元时间算法,用于在双马基游戏中找到统一的纳什平衡(Adario-Berry等人,2007年),下面的问题是:在双马基游戏上计算统一的纳什平衡有多难?本文解决这个问题。我们证明,决定非双马基游戏是否具有统一的纳什平衡的问题也是NP的完成。