Is having a unique equilibrium robust?

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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. © 2008 Elsevier B.V. All rights reserved.

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Viossat, Y. (2008). Is having a unique equilibrium robust? Journal of Mathematical Economics, 44(11), 1152–1160. https://doi.org/10.1016/j.jmateco.2007.06.008

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