Symmetric games with only asymmetric equilibria
It is known that not every symmetric game has a symmetric equilibrium because there are examples of symmetric games that fail to have any equilibria at all. But this leads to the following question: If a symmetric game has a Nash equilibrium, does it have a symmetric Nash equilibrium? In this Note, we show that the answer to this question is no by providing two examples of symmetric games that have only asymmetric equilibria.
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References listed on IDEAS
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- Kats, Amoz & Thisse, Jacques-Francois, 1992. "Unilaterally Competitive Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 21(3), pages 291-99.
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- Philip J. Reny, 1999. "On the Existence of Pure and Mixed Strategy Nash Equilibria in Discontinuous Games," Econometrica, Econometric Society, vol. 67(5), pages 1029-1056, September.
- Yang, Chun-Lei, 1994. "A simple extension of the Dasgupta-Maskin existence theorem for discontinuous games with an application to the theory of rent-seeking," Economics Letters, Elsevier, vol. 45(2), pages 181-183, June.
- Amir, Rabah & Garcia, Filomena & Knauff, Malgorzata, 2010. "Symmetry-breaking in two-player games via strategic substitutes and diagonal nonconcavity: A synthesis," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1968-1986, September.
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