Is Having a Unique Equilibrium Robust?
AbstractWe 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.
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Bibliographic InfoPaper provided by HAL in its series Post-Print with number hal-00361891.
Date of creation: Dec 2008
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Publication status: Published, Journal of Mathematical Economics, 2008, 44, 11, 1152-1160
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Correlated equilibrium; Linear duality; Unique equilibrium; Quasi-strict equilibrium;
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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.
- Aumann, Robert J., 1974.
"Subjectivity and correlation in randomized strategies,"
Journal of Mathematical Economics,
Elsevier, vol. 1(1), pages 67-96, March.
- R. Aumann, 2010. "Subjectivity and Correlation in Randomized Strategies," Levine's Working Paper Archive 389, David K. Levine.
- Ritzberger, Klaus, 1994. "The Theory of Normal Form Games form the Differentiable Viewpoint," International Journal of Game Theory, Springer, vol. 23(3), pages 207-36.
- 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, March.
- Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- Yannick Viossat, 2008.
"Evolutionary Dynamics May Eliminate All Strategies Used in Correlated Equilibria,"
- Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
- Viossat, Yannick, 2006. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Working Paper Series in Economics and Finance 629, Stockholm School of Economics, revised 21 Jun 2006.
- Lehrer, Ehud & Solan, Eilon & Viossat, Yannick, 2011.
"Equilibrium payoffs of finite games,"
Journal of Mathematical Economics,
Elsevier, vol. 47(1), pages 48-53, January.
- Forges, Françoise, 2012. "Correlated equilibria and communication in games," Open Access publications from UniversitÃ© Paris-Dauphine urn:hdl:123456789/171, Université Paris-Dauphine.
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