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arXiv · 2410.16548

On the Uniqueness of Nash Equilibria in Multiagent Matrix Games

James P. Bailey
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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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James P. Bailey. 2024-10-21. On the Uniqueness of Nash Equilibria in Multiagent Matrix Games. https://arxiv.org/abs/2410.16548

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