On Knots and Dynamics in Games∗

We extend Kohlberg and Mertens’ (1986) structure theorem concerning the Nash equilibrium correspondence to show that its graph is not only homeomorphic to the underlying space of games but that it is also unknotted. This is then shown to have some basic consequences for dynamics whose rest points are Nash equilibria. ∗We would like to thank Eddie Dekel and Joerg Oechssler for helpful comments and Jean-François Mertens for unfailing inspiration. We are grateful to CORE and to the School of Economics at Tel Aviv University for their generous hospitality. Germano also gratefully acknowledges financial support from the European Commission, Grant ERBFMBICT972857. All errors are ours. †Dipartimento di Matematica, Università degli Studi di Pavia, 27100 Pavia, Italy, and CORE, 34, Voie du Roman Pays, 1348 Louvain-la-Neuve, Belgium. ‡The Eitan Berglas School of Economics, Tel Aviv University, 69978 Tel Aviv, Israel.