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Auteurs principaux: Hou, Yuqing, Cao, Yiyin, Dang, Chuangyin
Format: Preprint
Publié: 2026
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Accès en ligne:https://arxiv.org/abs/2602.10524
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author Hou, Yuqing
Cao, Yiyin
Dang, Chuangyin
author_facet Hou, Yuqing
Cao, Yiyin
Dang, Chuangyin
contents Normal-form proper equilibrium, introduced by Myerson as a refinement of normal-form perfect equilibrium, occupies a distinctive position in the equilibrium analysis of extensive-form games because its more stringent perturbation structure entails the sequential rationality. However, the size of the normal-form representation grows exponentially with the number of parallel information sets, making the direct determination of normal-form proper equilibria intractable. To address this challenge, we develop a compact sequence-form proper equilibrium by redefining the expected payoffs over sequences, and we prove that it coincides with the normal-form proper equilibrium via strategic equivalence. To facilitate computation, we further introduce an alternative representation by defining a class of perturbed games based on an $\varepsilon$-permutahedron over sequences. Building on this representation, we introduce two differentiable path-following methods for computing normal-form proper equilibria. These methods rely on artificial sequence-form games whose expected payoff functions incorporate logarithmic or entropy regularization through an auxiliary variable. We prove the existence of a smooth equilibrium path induced by each artificial game, starting from an arbitrary positive realization plan and converging to a normal-form proper equilibrium of the original game as the auxiliary variable approaches zero. Finally, our experimental results demonstrate the effectiveness and efficiency of the proposed methods.
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spellingShingle Characterization and Computation of Normal-Form Proper Equilibria in Extensive-Form Games via the Sequence-Form Representation
Hou, Yuqing
Cao, Yiyin
Dang, Chuangyin
Computer Science and Game Theory
Normal-form proper equilibrium, introduced by Myerson as a refinement of normal-form perfect equilibrium, occupies a distinctive position in the equilibrium analysis of extensive-form games because its more stringent perturbation structure entails the sequential rationality. However, the size of the normal-form representation grows exponentially with the number of parallel information sets, making the direct determination of normal-form proper equilibria intractable. To address this challenge, we develop a compact sequence-form proper equilibrium by redefining the expected payoffs over sequences, and we prove that it coincides with the normal-form proper equilibrium via strategic equivalence. To facilitate computation, we further introduce an alternative representation by defining a class of perturbed games based on an $\varepsilon$-permutahedron over sequences. Building on this representation, we introduce two differentiable path-following methods for computing normal-form proper equilibria. These methods rely on artificial sequence-form games whose expected payoff functions incorporate logarithmic or entropy regularization through an auxiliary variable. We prove the existence of a smooth equilibrium path induced by each artificial game, starting from an arbitrary positive realization plan and converging to a normal-form proper equilibrium of the original game as the auxiliary variable approaches zero. Finally, our experimental results demonstrate the effectiveness and efficiency of the proposed methods.
title Characterization and Computation of Normal-Form Proper Equilibria in Extensive-Form Games via the Sequence-Form Representation
topic Computer Science and Game Theory
url https://arxiv.org/abs/2602.10524