On the Evolutionary Selection of Nash Equilibrium Components

Paper number: 01/06

Paper date: September 15, 2001

Year: 2001

Paper Category: Working Paper

Authors

Dieter Balkenborg and Karl H. Schlag

Abstract

It is well known for the common multi-population evolutionary dynamics applied to normal form games that a pure strategy combination is asymptotically stable if and only if it is a strict equilibrium point. We extend this result to sets as follows. For certain regular selection dynamics every connected and closed asymptotically stable set of rest points containing a pure strategy combination is a strict equilibrium set and hence a Nash equilibrium component. A converse statement holds for two person games, for convex strict equilibrium sets and for the standard replicator dynamic.

On the Evolutionary Selection of Nash Equilibrium Components On the Evolutionary Selection of Nash Equilibrium Components