Evolutionarily stable strategy

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In game theory and behavioural ecology, an evolutionarily stable strategy[1] (ESS) is a strategy which, if adopted by a population of players, cannot be invaded by any alternative strategy that is initially rare. An ESS is an equilibrium refinement of the Nash equilibrium -- it is a Nash equilibrium which is "evolutionarily" stable meaning that once it is fixed in a population, natural selection alone is sufficient to prevent alternative (mutant) strategies from successfully invading.

The ESS was developed in order to define a class of solutions to game theoretic problems, equivalent to the Nash equilibrium, but which could be applied to the evolution of social behaviour in animals. Nash equilibria may sometimes exist due to the application of rational foresight, which would be inappropriate in an evolutionary context. Teleological forces such as rational foresight cannot explain the outcomes of trial-and-error processes, such as evolution, and thus have no place in biological applications. The definition of an ESS excludes such Nash equilibria.

First developed in 1973, the ESS has come to be widely used in behavioural ecology and economics, and has been used in anthropology, evolutionary psychology, philosophy, and political science.



Evolutionarily stable strategies were defined and introduced by John Maynard Smith and George R. Price in a 1973 Nature paper.[2] Such was the time taken in peer-reviewing the paper for Nature that this was preceded by a 1972 essay by Maynard Smith contained in a book of essays entitled On Evolution.[3] The 1972 essay is sometimes cited instead of the 1973 paper, but while university libraries almost certainly contain copies of Nature, the book is more obscure. Nature papers are usually short, and Maynard Smith published a lengthier paper in the Journal of Theoretical Biology in 1974.[4] A further explanation is to be found in Maynard Smith's 1982 book Evolution and the Theory of Games[5] — sometimes these are cited instead. In fact, the ESS has become so central to game theory that often no citation is given as it is assumed the reader has knowledge of it already and therefore no need for further reading. Maynard Smith mathematically formalised a verbal argument made by Price that he came across while peer-reviewing Price's paper, offering to make Price co-author of the Nature paper when it became apparent that the somewhat disorganised Price was not ready to revise his article to make it suitable for publication.

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