On (Un)Knots and Dynamics in Games

Posted: 29 Mar 2005

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

We extend Kohlberg and Mertens' (1986) structure theorem on the Nash correspondence to show that its graph is not only homeomorphic to the underlying space of games, but that the homeomorphism extends to the ambient space of games times strategies, thus implying the graph is unknotted. This has several consequences for dynamics whose rest points are Nash equilibria. In particular, a homotopy property is established that allows to determine whether Nash equilibria or components of Nash equilibria - based directly on their local geometry on the graph - may be stable under a wide class of dynamics.

Keywords: Geometry of Nash equilibria, learning mixed equilibria, index, degree, knot, dynamics, stability

JEL Classification: C61, C62, C72

Suggested Citation

Demichelis, Stefano and Germano, Fabrizio, On (Un)Knots and Dynamics in Games. Available at SSRN: https://ssrn.com/abstract=678641

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)

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