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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