Is Having a Unique Equilibrium Robust?
Viossat, Yannick (2008), Is Having a Unique Equilibrium Robust?, Journal of Mathematical Economics, 44, 11, p. 1152-1160. http://dx.doi.org/10.1016/j.jmateco.2007.06.008
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00361891/en/
Journal nameJournal of Mathematical Economics
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Abstract (EN)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.
Subjects / KeywordsCorrelated equilibrium; Linear duality; Unique equilibrium; Quasi-strict equilibrium
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