On the Evolutionary Selection of Nash Equilibrium Components
Paper number: 01/06
Paper date: September 15, 2001
Paper Category: Working Paper
Dieter Balkenborg and Karl H. Schlag
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.