Symmetric Games Revisited

28 Pages Posted: 30 Jul 2015 Last revised: 13 Jul 2018

See all articles by Zhigang Cao

Zhigang Cao

Beijing Jiaotong University - School of Economics and Management

Xiaoguang Yang

Chinese Academy of Sciences (CAS)

Date Written: June 17, 2018


We distinguish among three types of symmetric games, which we name ordinary symmetric games, renaming symmetric games, and name-irrelevant symmetric games, in an order of increasing broadness. The second class of symmetric games is new and has bite even on some elementary two by two games, e.g., Battle of Sexes is renaming symmetric but not ordinary symmetric, and Matching Pennies is name-irrelevant symmetric but not renaming symmetric. When each player has two strategies, both ordinary and renaming symmetric games are exact potential games, a property not possessed by their name-irrelevant counterparts. We establish a characterization of the renaming symmetric game through the player symmetry group.

Keywords: Symmetric games, Potential games,Symmetry groups

JEL Classification: C72

Suggested Citation

Cao, Zhigang and Yang, Xiaoguang, Symmetric Games Revisited (June 17, 2018). Mathematical Social Sciences, Forthcoming. Available at SSRN: or

Zhigang Cao

Beijing Jiaotong University - School of Economics and Management ( email )


Xiaoguang Yang (Contact Author)

Chinese Academy of Sciences (CAS) ( email )

52 Sanlihe Rd.
Datun Road, Anwai
Beijing, Xicheng District 100864

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