On the Uniqueness of Nash Equilibria in Multiagent Matrix Games
Computer Science and Game Theory
2024-10-23 v1
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.
Cite
@article{arxiv.2410.16548,
title = {On the Uniqueness of Nash Equilibria in Multiagent Matrix Games},
author = {James P. Bailey},
journal= {arXiv preprint arXiv:2410.16548},
year = {2024}
}