Notes on Equilibria in Symmetric Games

• Main Authors: CHENG, Shih-Fen, REEVES, Daniel M., VOROBEYCHIK, Yevgeniy, WELLMAN, Michael P.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2004
• Subjects: Artificial Intelligence and Robotics; Business; Operations Research, Systems Engineering and Industrial Engineering
• Online Access: https://ink.library.smu.edu.sg/sis_research/1213; https://ink.library.smu.edu.sg/context/sis_research/article/2212/viewcontent/ChengSF_2004_EquilibriaSymmetricGames.pdf
• Institution: Singapore Management University

In a symmetric game, every player is identical with respect to the game rules. We show that a symmetric 2strategy 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.