Is having a unique equilibrium robust?

Yannick Viossat

Journal of Mathematical Economics, 2008, vol. 44, issue 11, 1152-1160

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.

Keywords: Correlated; equilibrium; Linear; duality; Unique; equilibrium; Quasi-strict; equilibrium (search for similar items in EconPapers)
Date: 2008
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:44:y:2008:i:11:p:1152-1160

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