On the Indices of Zeros of Nash Fields

Posted: 26 Jun 2003

See all articles by Stefano Demichelis

Stefano Demichelis

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE)

Fabrizio Germano

Universitat Pompeu Fabra - Department of Economics and Business

Abstract

This paper shows a fundamental property of vector fields representing dynamics on spaces of mixed strategies of normal form games whose zeros coincide with the Nash equilibria of the underlying games. The property shown is that the indices of components of zeros of any vector field in this class coincide with the local degrees of the projection map, mapping from the graph of the Nash equilibrium correspondence onto the space of games, evaluated at the corresponding components of Nash equilibria. This property is important since it implies that, for a large class of dynamics, the indices of components of zeros are completely determined by the geometry of the Nash equilibrium correspondence, thus providing a further link between evolutionary game theory, the theory of equilibrium refinements, and the geometry of Nash equilibrium.

JEL Classification: C70, C72

Suggested Citation

Demichelis, Stefano and Germano, Fabrizio, On the Indices of Zeros of Nash Fields. Available at SSRN: https://ssrn.com/abstract=419466

Stefano Demichelis

Catholic University of Louvain (UCL) - Center for Operations Research and Econometrics (CORE) ( email )

34 Voie du Roman Pays
B-1348 Louvain-la-Neuve, b-1348
Belgium

Fabrizio Germano (Contact Author)

Universitat Pompeu Fabra - Department of Economics and Business ( email )

Ramon Trias Fargas 25-27
Barcelona, 08005
Spain
+34-93-542-2729 (Phone)
+34-93-542-1746 (Fax)

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Abstract Views
693
PlumX Metrics