Is Having a Unique Equilibrium Robust?

Details Is Having a Unique Equilibrium Robust? Is Having a Unique Equilibrium Robust?

2009-02-16

arxiv.org/abs/0902.2771v1

Journal of Mathematical Economics 44, 11 (2008) 1152-1160

Mathematics

Optimization and Control

Scientific paper

10.1016/j.jmateco.2007.06.008

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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