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Article Dans Une Revue Journal of Mathematical Economics Année : 2008

Is Having a Unique Equilibrium Robust?

Résumé

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.
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Dates et versions

hal-00361891 , version 1 (16-02-2009)

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Yannick Viossat. Is Having a Unique Equilibrium Robust?. Journal of Mathematical Economics, 2008, 44 (11), pp.1152-1160. ⟨10.1016/j.jmateco.2007.06.008⟩. ⟨hal-00361891⟩
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