Is Having a Unique Equilibrium Robust?
Optimization and Control
2009-02-17 v1
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.
Cite
@article{arxiv.0902.2771,
title = {Is Having a Unique Equilibrium Robust?},
author = {Yannick Viossat},
journal= {arXiv preprint arXiv:0902.2771},
year = {2009}
}