Dominated Actions in Imperfect-Information Games

• URL: http://arxiv.org/abs/2504.09716v1
• Date: Sun, 13 Apr 2025 20:48:44 GMT
• Title: Dominated Actions in Imperfect-Information Games
• Authors: Sam Ganzfried,
• Abstract summary: We define and study the concept of dominated actions in imperfect-information games.<n>Our main result is a empirically-time algorithm for determining whether an action is dominated by any mixed strategy.<n>We explore the role of dominated actions in the "All In or Fold" No-Limit Texas Hold'em poker variant.
• Score: 0.4895118383237099
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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