AI 中文总结
本文针对带参数不确定性的同时行动博弈，研究事后均衡（EPEs）的结构，刻画其性质，引入最优近似EPEs概念，分析其在零和博弈与凹势博弈中的计算问题并给出相关结果。
AI 中文摘要
本文研究带有参数不确定性的同时行动博弈中的事后均衡（ex-post equilibria，EPEs）。我们首先将EPEs与现有鲁棒均衡概念进行比较，为EPEs作为带参数不确定性博弈的解概念提供了一般基础，并证明EPEs可由两个博弈论性质（单调性与集合一致性）完全刻画。由于事后均衡可能不存在，我们引入最优近似事后均衡的概念，其中参与者采用近似最优反应同时最小化次优程度。我们研究EPEs与最优近似EPEs的计算问题，聚焦两类重要博弈：零和博弈与凹势博弈。我们给出若干复杂性结果，以及基于辅助极小极大公式的通用计算方法。
英文摘要
This paper studies ex-post equilibria (EPEs) in simultaneous-move games with parameter uncertainty. We first compare EPEs with existing notions of robust equilibrium and provide a general foundation for EPEs as a solution concept for games with parameter uncertainty, and we show that EPEs are fully characterized by two game-theoretic properties (monotonicity and set-consistency). Since ex-post equilibria may fail to exist, we introduce the notion of an optimal approximate ex-post equilibrium, in which players adopt approximate best responses while minimizing the degree of suboptimality. We study the problem of computing EPEs and optimal approximate EPEs, focusing on two important classes of games: zero-sum games and concave potential games. We provide several hardness results, as well as a general class of computational approaches based on auxiliary minimax formulations.
