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Evolutionarily Robust Strategies: Two Nontrivial Examples and a Theorem
, Bernhard Pierre
Published in Birkhäuser Boston
2009
Pages: 1 - 19
Abstract

We revisit the relationship between evolutionarily stable strategy (ESS) and related topics such as evolutionarily robust strategy (ERS) on the one hand, and stability of the replicator dynamics on the other hand, when the phenotypic set is continuous. The state of the population considered is a measure over the phenotypic set. Thus, topological considerations come into play that make the situation much more difficult than for a finite phenotypic set. As a consequence, the issue of the asymptotic stability of an ERS is not settled at this time. We give one partial new result in that direction.

It has also been noticed in the literature that there is a dearth of concrete examples of mixed ESS or ERS in the literature. Actually none seems to be knownif the “kernel” of the game is continuous.We provide two such examples, one a convex combination of two Dirac measures and one family with the Lebesgue measure as an ERS.

About the journal
JournalAdvances in Dynamic Games and Their Applications
PublisherBirkhäuser Boston
Open AccessNo