Is Having a Unique Equilibrium Robust?
Abstract
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.Download Info
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Paper provided by HAL in its series Post-Print with number hal-00361891.Length:
Date of creation: Dec 2008
Date of revision:
Publication status: Published, Journal of Mathematical Economics, 2008, 44, 11, 1152-1160
Handle: RePEc:hal:journl:hal-00361891
Note: View the original document on HAL open archive server: http://hal.archives-ouvertes.fr/hal-00361891/en/
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Related research
Keywords: Correlated equilibrium; Linear duality; Unique equilibrium; Quasi-strict equilibrium;Other versions of this item:
- Viossat, Yannick, 2008. "Is having a unique equilibrium robust?," Journal of Mathematical Economics, Elsevier, vol. 44(11), pages 1152-1160, December.
- NEP-ALL-2009-02-28 (All new papers)
- NEP-GTH-2009-02-28 (Game Theory)
References
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Citations
Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.Cited by:
- 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 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.
- Ehud Lehrer & Eilon Solan & Yannick Viossat, 2011. "Equilibrium payoffs in finite games," Post-Print hal-00361914, HAL.
- Forges, Françoise, 2012. "Correlated equilibria and communication in games," Open Access publications from Université Paris-Dauphine urn:hdl:123456789/171, Université Paris-Dauphine.
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