Oddness of the number of Nash equilibria: the Case of Polynomial Payoff Functions

Philippe Bich () and Julien Fixary ()
Additional contact information
Philippe Bich: Centre d'Economie de la Sorbonne, Paris School of Economics, https://bichgame.wordpress.com/
Julien Fixary: Centre d'Economie de la Sorbonne, Université Paris 1 Panthéon-Sorbonne, https://centredeconomiesorbonne.cnrs.fr

Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne

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 payoff 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)
JEL-codes: C02 C62 C72 D85 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2021-08
New Economics Papers: this item is included in nep-cwa, nep-gth and nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://mse.univ-paris1.fr/pub/mse/CES2021/21027.pdf (application/pdf)
https://halshs.archives-ouvertes.fr/halshs-03354269

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:mse:cesdoc:21027

Access Statistics for this paper

More papers in Documents de travail du Centre d'Economie de la Sorbonne from Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne Contact information at EDIRC.
Bibliographic data for series maintained by Lucie Label ().