On the Uniqueness of Nash Equilibria in Multiagent Matrix Games

2024/10/21 by James P. Bailey, Bailey, James P. · 1 citation
Decision Sciences · Economics, Econometrics and Finance · #Auction Theory and Applications #Computer Science and Game Theory (cs.GT) #Economic theories and models #FOS: Computer and information sciences #Game Theory and Applications

paper · pdf · doi:10.48550/arxiv.2410.16548

openalex publication_date 2024/10/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We provide a complete characterization for uniqueness of equilibria in unconstrained polymatrix games. We show that while uniqueness is natural for coordination and general polymatrix games, zero-sum games require that the dimension of the combined strategy space is even. Therefore, non-uniqueness is common in zero-sum polymatrix games. In addition, we study the impact of non-uniqueness on classical learning dynamics for multiagent systems and show that the classical methods still yield unique estimates even when there is not a unique equilibrium.

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• Higher-Order Uncoupled Learning Dynamics and Nash Equilibrium

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