发表机构
National Technical University of Athens; Archimedes, Athena Research Center; University of California, Irvine; National and Kapodistrian University of Athens（雅典国立技术大学; 阿尔基米德，雅典研究中心; 加州大学尔湾分校; 雅典国家与卡波季斯特里乌斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明，在非退化双矩阵博弈中寻找Shapley指标为+1的精确纳什均衡是PPADS完全的，这是首个基于显式收益矩阵的此类问题，解决了Daskalakis的开放问题。
AI 中文摘要
每一个非退化双矩阵博弈都有一个Shapley指标为+1的纳什均衡，因为所有均衡都是孤立的，指标为+1或-1，且它们的指标之和为+1。我们证明以下承诺搜索问题是PPADS完全的：给定一个承诺为非退化的有理双矩阵博弈，找到一个指标为+1的精确纳什均衡。据我们所知，这是第一个实例为显式有理正规型收益矩阵而非简洁电路或图灵机的PPADS完全均衡搜索问题，从而解决了Daskalakis提出的一个开放问题[Daskalakis, 2019]。
英文摘要
Every nondegenerate bimatrix game has a Nash equilibrium of Shapley index +1, since all equilibria are isolated, have index +1 or -1, and their indices sum to +1. We prove that the following promise search problem is PPADS-complete: given a rational bimatrix game promised to be nondegenerate, find an exact Nash equilibrium of index +1. The nondegeneracy promise can be removed if nonregular equilibria are also accepted: finding either a regular Nash equilibrium of index +1 or a nonregular Nash equilibrium in an arbitrary rational bimatrix game is also PPADS-complete. To our knowledge, this is the first PPADS-complete equilibrium search problem whose instances are explicit rational normal form payoff matrices, rather than succinct circuits or Turing machines, and thereby addresses an open question posed by Daskalakis [Daskalakis, 2019].
