Dominance is a fundamental concept in game theory. In strategic-form games dominated strategies can be identified in polynomial time. As a consequence, iterative removal of dominated strategies can be performed efficiently as a preprocessing step for reducing the size of a game before computing a Nash equilibrium. For imperfect-information games in extensive form, we could convert the game to strategic form and then iteratively remove dominated strategies in the same way; however, this conversion may cause an exponential blowup in game size. In this paper we define and study the concept of dominated actions in imperfect-information games. Our main result is a polynomial-time algorithm for determining whether an action is dominated (strictly or weakly) by any mixed strategy in n-player games, which can be extended to an algorithm for iteratively removing dominated actions. This allows us to efficiently reduce the size of the game tree as a preprocessing step for Nash equilibrium computation. We explore the role of dominated actions empirically in the "All In or Fold" No-Limit Texas Hold'em poker variant.

翻译：占优是博弈论中的一个基本概念。在策略型博弈中，占优策略可以在多项式时间内被识别。因此，在计算纳什均衡之前，可以高效地执行迭代剔除占优策略作为缩减博弈规模的预处理步骤。对于扩展型的不完全信息博弈，我们可以将博弈转换为策略型，然后以相同方式迭代剔除占优策略；然而，这种转换可能导致博弈规模呈指数级膨胀。本文定义并研究了不完全信息博弈中占优行动的概念。我们的主要成果是：针对n人博弈，提出了一个多项式时间算法，用于判定一个行动是否被任意混合策略占优（严格或弱占优），该算法可扩展为迭代剔除占优行动的算法。这使得我们能够高效地缩减博弈树规模，作为纳什均衡计算的预处理步骤。我们通过“全押或弃牌”无限注德州扑克变体，对占优角色的作用进行了实证探索。