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|
|Date of revision:|
|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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