Is Having a Unique Equilibrium Robust?

Yannick Viossat

Post-Print from HAL

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: 2008-12
Note: View the original document on HAL open archive server: https://hal.science/hal-00361891v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

Published in Journal of Mathematical Economics, 2008, 44 (11), pp.1152-1160. ⟨10.1016/j.jmateco.2007.06.008⟩

Downloads: (external link)
https://hal.science/hal-00361891v1/document (application/pdf)

Related works:
Journal Article: Is having a unique equilibrium robust? (2008)
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:hal-00361891

DOI: 10.1016/j.jmateco.2007.06.008

Access Statistics for this paper

More papers in Post-Print from HAL
Bibliographic data for series maintained by CCSD ().