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In Game Theory and Behavioural Ecology , an evolutionarily stable strategy (or '''ESS'''; also '''evolutionary stable strategy''') is a Strategy which, if adopted by a Population of players, cannot be invaded by any alternative strategy. An ESS is an Equilibrium Refinement to a Nash Equilibrium (a strategy set which — if adopted by all players in a game — results in everyone doing at least as well as they could by unilaterally deviating). An ESS is a Nash equilibrium which is "evolutionarily" stable in that, once Fixed in a population, it cannot be altered by the evolutionary forces of Mutation and Natural Selection . 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 . An ESS excludes Nash equilibria dependent upon foresight, and includes only those Equilibria which are Stable if Natural Selection is assumed to be the only force acting on strategy choice. 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 . HISTORY Evolutionarily stable strategies were defined and introduced by '' John Maynard Smith . (1982) '' Evolution And The Theory Of Games ''. ISBN 0-521-28884-3. The concept was derived from 's W.D. Hamilton (1967) Extraordinary sex ratios. '' Science '' 156, 477-488. work on Sex Ratio s, especially Hamilton's (1967) concept of an Unbeatable Strategy . The idea can be traced back to Ronald Fisher Ronald Fisher (1930) '' The Genetical Theory Of Natural Selection ''. Clarendon Press, Oxford. and Charles Darwin (1859) Charles Darwin (1859). '' On The Origin Of Species ''. Maynard Smith was jointly awarded the 1999 Crafoord Prize for his development of the concept of evolutionary stable strategies, and the application of game theory to the evolution of behaviour The 1999 Crafoord Prize press release . The ESS was first used in the Social Sciences by Robert Axelrod in his 1984 book '' The Evolution Of Cooperation ''. Since that time, there has been widespread use in the social sciences, including work in Anthropology , Economics , Philosophy , and Political Science . In these fields the primary interest is not in an ESS as the end of Biological evolution, but as an end point in the process of Cultural Evolution or individual learning.1 In contrast, the ESS is used in Evolutionary Psychology primarily as a model for Human Biological Evolution . MOTIVATION The Nash Equilibrium is the traditional Solution Concept in Game Theory . It is traditionally underwritten by appeals to the cognitive abilities of the players. Authors often presume that individuals are aware of the structure of the game, are consciously attempting to maximize their returns, and are attempting to predict the moves of their opponents. In addition, they presume that all of this is Common Knowledge between the players. These facts are then used to explain why players will choose Nash equilibrium strategies. Evolutionarily stable strategies are motivated entirely differently. Here, it is presumed that the players are individuals with biologically encoded, Heritable strategies. The individuals have no control over the strategy they play and need not even be capable of being aware of the game. The individuals reproduce and are subject to the forces of Natural Selection (with the Payoffs of the game representing biological Fitness ). It is imagined that the alternative strategies of the game occasionally occur, via a process like Mutation , and in order to be an ESS a strategy must be resistant to these mutations. Given the radically different motivating assumptions, it may come as a surprise that ESSes and Nash equilibria often coincide. In fact, every ESS corresponds to a Nash equilibrium, but there are some Nash equilibria that are not ESSes. NASH EQUILIBRIA AND ESS |
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