S-F Cheng, DM Reeves, Y Vorobeychik, and MP Wellman
AAMAS-04 Workshop on Game-Theoretic and Decision-Theoretic Agents, July 2004.
In a symmetric game, every player is identical with respect to the game rules. We show that a symmetric 2-strategy game must have a pure-strategy Nash equilibrium. We also discuss Nash’s original paper and its generalized notion of symmetry in games. As a special case of Nash’s theorem, any finite symmetric game has a symmetric Nash equilibrium. Furthermore, symmetric infinite games with compact, convex strategy spaces and continuous, quasiconcave utility functions have symmetric pure-strategy Nash equilibria. Finally, we discuss how to exploit symmetry for more efficient methods of finding Nash equilibria.