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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- Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414, July.
- Becker, Johannes Gerd & Damianov, Damian S., 2006. "On the existence of symmetric mixed strategy equilibria," Economics Letters, Elsevier, vol. 90(1), pages 84-87, January.
- 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.
- Kats, Amoz & Thisse, Jacques-Francois, 1992.
"Unilaterally Competitive Games,"
International Journal of Game Theory,
Springer;Game Theory Society, vol. 21(3), pages 291-299.
- Kats, A. & Thisse, J.-F., "undated". "Unilaterally competitive games," CORE Discussion Papers RP 1039, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Aumann, Robert J. & Sorin, Sylvain, 1989. "Cooperation and bounded recall," Games and Economic Behavior, Elsevier, vol. 1(1), pages 5-39, March.
- Partha Dasgupta & Eric Maskin, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Oxford University Press, vol. 53(1), pages 1-26.
- 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. Full references (including those not matched with items on IDEAS)