Oddness of the number of Nash equilibria: the case of polynomial payoff functions

Philippe Bich () and Julien Fixary ()
Additional contact information
Philippe Bich: UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement
Julien Fixary: UP1 - Université Paris 1 Panthéon-Sorbonne, CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

Post-Print from HAL

Abstract: In 1971, Robert Wilson ([19]) proved that "almost all" finite games have an odd number of mixed Nash equilibria (oddness theorem). Since then, several other proofs have been given, but always for mixed extensions of finite games. In this paper, we prove oddness theorem for large classes of polynomial payo↵ functions and semi-algebraic sets of strategies, and we provide some applications to recent models.

Keywords: Nash equilibria; polynomial payoff functions; generic oddness (search for similar items in EconPapers)
Date: 2021-08-30
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03354269v1
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Published in 2021

Downloads: (external link)
https://shs.hal.science/halshs-03354269v1/document (application/pdf)

Related works:
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:halshs-03354269

Access Statistics for this paper

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