On the evolutionary selection of sets of Nash equilibria

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 se...

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Bibliographic Details
Published in:Journal of economic theory 2007-03, Vol.133 (1), p.295-315
Main Authors: Balkenborg, Dieter, Schlag, Karl H.
Format: Article
Language:English
Subjects:
Asymptotic methods
Economic theory
Equilibrium
Evolutionary dynamics
Evolutionary economics
Game theory
Nash equilibrium
Nash equilibrium component
Regular selection dynamics
Replicator dynamic
Strict equilibrium set
Studies
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Summary: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.
ISSN:0022-0531
1095-7235
DOI:10.1016/j.jet.2005.08.008