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 inJournal of economic theory Vol. 133; no. 1; pp. 295 - 315
Main Authors Balkenborg, Dieter, Schlag, Karl H.
Format Journal Article
LanguageEnglish
Published New York Elsevier Inc 01.03.2007
Elsevier
Elsevier Science Publishing Company, Inc
SeriesJournal of Economic Theory
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
C79
Strict equilibrium set
Nash equilibrium component
Regular selection dynamics
Evolutionary dynamics
C72
Replicator dynamic
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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.
Bibliography:ObjectType-Article-2
SourceType-Scholarly Journals-1
ObjectType-Feature-1
content type line 23
ISSN:0022-0531
1095-7235
DOI:10.1016/j.jet.2005.08.008