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：支配是博弈论中的基本概念。在正规式博弈中，支配策略可在多项式时间内识别。因此，迭代删除支配策略可作为计算纳什均衡前缩减博弈规模的有效预处理步骤。对于扩展式不完全信息博弈，我们可将博弈转化为正规式，进而以相同方式迭代删除支配策略；然而，这种转化可能导致博弈规模指数级增长。本文定义并研究了不完全信息博弈中的支配行动概念。我们的主要成果是：在具有公开可观测行动的双人完美回忆博弈中，提出一种多项式时间算法，用于判定某一行动是否被任意混合策略（严格或弱）支配，该算法可扩展至迭代删除支配行动。这使我们能在计算纳什均衡前，作为预处理步骤高效缩减博弈树规模。我们通过"全押或弃牌"无限注德州扑克对支配行动的作用进行了实证探索。