Notes on Equilibria in Symmetric Games

Notes on Equilibria in Symmetric Games

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 sy...

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Bibliographic Details
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
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Institution: Singapore Management University
Language: English
Description
Summary: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.

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