On the Evolutionary Selection of Sets of Nash Equilibria
Title: On the Evolutionary Selection of Sets of Nash Equilibria
Citation: Journal of Economic Theory, 2007, 131, 1, 295-315
It is well established for evolutionary dynamics in asymmetric games that a pure strategy combination is asymptotically stable if and only if it is a strict Nash equilibrium. We use an extension of the notion of a strict Nash equilibrium to sets of strategy combinations called strict equilibrium set and show the following. For a large class of evolutionary dynamics, including all monotone regular selection dynamics, every asymptotically stable set of rest points that contains a pure strategy combination in each of its connected components is a strict equilibrium set. A converse statement holds for two-person games, for convex sets and for the standard replicator dynamic.
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