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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by HAL in its series Post-Print with number hal-00361891.
Date of creation: Dec 2008
Date of revision:
Publication status: Published, Journal of Mathematical Economics, 2008, 44, 11, 1152-1160
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00361891/en/
Contact details of provider:
Web page: http://hal.archives-ouvertes.fr/
Correlated equilibrium; Linear duality; Unique equilibrium; Quasi-strict equilibrium;
Other versions of this item:
- C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
This paper has been announced in the following NEP Reports:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Forges, Francoise, 1990. "Correlated Equilibrium in Two-Person Zero-Sum Games," Econometrica, Econometric Society, vol. 58(2), pages 515, March.
- Nau, Robert F. & McCardle, Kevin F., 1990. "Coherent behavior in noncooperative games," Journal of Economic Theory, Elsevier, vol. 50(2), pages 424-444, April.
- 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., . "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.
- Roger B. Myerson, 1995.
"Dual Reduction and Elementary Games,"
1133, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- Noa Nitzan, 2005. "Tight Correlated Equilibrium," Discussion Paper Series dp394, The Center for the Study of Rationality, Hebrew University, Jerusalem.
- 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.
- Lehrer, Ehud & Solan, Eilon & Viossat, Yannick, 2011.
"Equilibrium payoffs of finite games,"
Journal of Mathematical Economics,
Elsevier, vol. 47(1), pages 48-53, January.
- Lehrer, Ehud & Solan, Eilon & Viossat, Yannick, 2011. "Equilibrium payoffs of finite games," Economics Papers from University Paris Dauphine 123456789/2960, Paris Dauphine University.
- Ehud Lehrer & Eilon Solan & Yannick Viossat, 2011. "Equilibrium payoffs in finite games," Post-Print hal-00361914, HAL.
- Viossat, Yannick, 2010.
"Properties and applications of dual reduction,"
Economics Papers from University Paris Dauphine
123456789/882, Paris Dauphine University.
- 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.
- Viossat, Yannick, 2008. "Evolutionary dynamics may eliminate all strategies used in correlated equilibrium," Mathematical Social Sciences, Elsevier, vol. 56(1), pages 27-43, July.
- Yannick Viossat, 2008. "Evolutionary Dynamics May Eliminate All Strategies Used in Correlated Equilibria," Post-Print hal-00360756, HAL.
- Viossat, Yannick, 2008. "Evolutionary Dynamics May Eliminate All Strategies Used in Correlated Equilibria," Economics Papers from University Paris Dauphine 123456789/1119, Paris Dauphine University.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (CCSD).
If references are entirely missing, you can add them using this form.