On the Evolutionary Selection of Nash Equilibrium Components

Dieter Balkenborg and Karl Schlag

No 106, Discussion Papers from University of Exeter, Department of Economics

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.

Keywords: evolutionary dynamics; replicator dynamic; regular selection dynamics; strict equilibrium set; Nash equilibrium component. (search for similar items in EconPapers)
JEL-codes: C79 (search for similar items in EconPapers)
Date: 2001-09
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