Dominance is a fundamental concept in game theory. In normal-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 normal 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 two-player perfect-recall games with publicly observable actions, which can be extended to iteratively remove 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 ``All In or Fold'' No-Limit Texas Hold'em poker.

翻译：支配是博弈论中的一个基本概念。在标准型博弈中，被支配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被支配策略作为预处理步骤来缩减博弈规模。对于扩展型不完全信息博弈，我们可以将博弈转换为标准型，然后以相同方式迭代剔除被支配策略；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的被支配行动概念。我们的主要成果是提出一个多项式时间算法，用于在具有公开可观察行动的两人完美回忆博弈中，判定某个行动是否被任意混合策略支配（严格或弱支配），该算法可扩展用于迭代剔除被支配行动。这使得我们能够高效缩减博弈树规模，作为纳什均衡计算的预处理步骤。我们通过“全押或弃牌”无限注德州扑克的实证研究探讨了被支配行动的作用。