International Journal of Game Theory

, Volume 45, Issue 3, pp 719–729 | Cite as

Pure strategy equilibrium in finite weakly unilaterally competitive games

  • Takuya Iimura
  • Takahiro Watanabe
Original Paper


We consider the finite version of the weakly unilaterally competitive game (Kats and Thisse, in Int J Game Theory 21:291–299, 1992) and show that this game possesses a pure strategy Nash equilibrium if it is symmetric and quasiconcave (or single-peaked). The first implication of this result is that unilaterally competitive or two-person weakly unilaterally competitive finite games are solvable in the sense of Nash, in pure strategies. We also characterize the set of equilibria of these finite games. The second implication is that there exists a finite population evolutionarily stable pure strategy equilibrium in a finite game, if it is symmetric, quasiconcave, and weakly unilaterally competitive.


Weakly unilaterally competitive game Finite game Symmetric game Quasiconcave game Existence of a pure strategy equilibrium Solvable game 

JEL Classification

C72 (Noncooperative game) 



The authors thank two anonymous reviewers for their valuable comments and suggestions. This work is supported by JSPS Grant-in-Aid for Scientific Research (C) (KAKENHI) 25380233.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Business AdministrationTokyo Metropolitan UniversityTokyoJapan

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