Is Having a Unique Equilibrium Robust?
We investigate whether having a unique equilibrium (or a given number of equilibria) is robust to perturbation of the payoffs, both for Nash equilibrium and correlated equilibrium. We show that the set of n-player finite games with a unique correlated equilibrium is open, while this is not true of Nash equilibrium for n>2. The crucial lemma is that a unique correlated equilibrium is a quasi-strict Nash equilibrium. Related results are studied. For instance, we show that generic two-person zero-sum games have a unique correlated equilibrium and that, while the set of symmetric bimatrix games with a unique symmetric Nash equilibrium is not open, the set of symmetric bimatrix games with a unique and quasi-strict symmetric Nash equilibrium is.
|Date of creation:||Dec 2008|
|Publication status:||Published in Journal of Mathematical Economics, Elsevier, 2008, 44 (11), pp.1152-1160. <10.1016/j.jmateco.2007.06.008>|
|Note:||View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00361891|
|Contact details of provider:|| Web page: https://hal.archives-ouvertes.fr/|
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- Myerson, Roger B., 1997.
"Dual Reduction and Elementary Games,"
Games and Economic Behavior,
Elsevier, vol. 21(1-2), pages 183-202, October.
- Roger B. Myerson, 1995. "Dual Reduction and Elementary Games," Discussion Papers 1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Aumann, Robert J., 1974. "Subjectivity and correlation in randomized strategies," Journal of Mathematical Economics, Elsevier, vol. 1(1), pages 67-96, March.
- AUMANN, Robert J., "undated". "Subjectivity and correlation in randomized strategies," CORE Discussion Papers RP 167, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
- Sergiu Hart & David Schmeidler, 2013. "Existence Of Correlated Equilibria," World Scientific Book Chapters, in: Simple Adaptive Strategies From Regret-Matching to Uncoupled Dynamics, chapter 1, pages 3-14 World Scientific Publishing Co. Pte. Ltd..
- Sergiu Hart & David Schmeidler, 1989. "Existence of Correlated Equilibria," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 18-25, February.
- Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer;Game Theory Society, vol. 23(3), pages 207-236.
- Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
- Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515-515, March.
- FORGES, Françoise, "undated". "Correlated equilibrium in two-person zero-sum games," CORE Discussion Papers RP 883, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem. Full references (including those not matched with items on IDEAS)