Technology Category
Game Theory and Economic Paradigms: Imperfect InformationSearch and Optimization: Adversarial SearchMultiagent Systems: Mechanism Design
Dominated Actions in Imperfect-Information Games
🤖 AI Summary
Solving for Nash equilibria in incomplete-information extensive-form games is hindered by exponential growth of the strategy space. Method: This paper formally defines “dominated actions” in extensive-form games and proposes a polynomial-time algorithm—combining linear programming with game-tree traversal—to rigorously identify both strictly and weakly dominated actions under mixed strategies. The method enables iterative pruning directly on the extensive-form representation, avoiding conversion to the exponentially larger normal-form representation. Crucially, it incorporates action-feasibility constraints (e.g., “All-In or Fold” in poker) to ensure correctness and practical applicability. Contribution/Results: The preprocessing step significantly reduces game size and accelerates equilibrium computation. Theoretically, the dominance detection is proven complete, with worst-case time complexity polynomial in the size of the game tree. Experimental results confirm substantial scalability improvements across benchmark games.
Technology Category
Application Category
📝 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.
Problem
Research questions and friction points this paper is trying to address.
Identifying dominated actions in imperfect-information games efficiently
Reducing game tree size via iterative removal of dominated actions
Enabling preprocessing for Nash equilibrium computation in large games
Innovation
Methods, ideas, or system contributions that make the work stand out.
Polynomial-time algorithm for dominated actions
Iterative removal of dominated actions
Efficient game tree reduction preprocessing
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