evolutionarily stable strategy (ESS)

An evolutionarily stable strategy (ESS) is a strategy (or set of strategies) which, if adopted by a population in a given environment, is impenetrable, meaning that it cannot be invaded by any alternative strategy (or strategies) that are initially rare. It is relevant in game theory, behavioural ecology, and evolutionary psychology. An ESS is an equilibrium refinement of the Nash equilibrium. It is a Nash equilibrium that is "evolutionarily" stable: once it is fixed in a population, natural selection alone is sufficient to prevent alternative (mutant) strategies from invading successfully. The theory is not intended to deal with the possibility of gross external changes to the environment that bring new selective forces to bear.

First published as a specific term in the 1972 book by John Maynard Smith,[1] the ESS is widely used in behavioural ecology and economics, and has been used in anthropology, evolutionary psychology, philosophy, and political science.

Contents

• 1 History

• 2 Motivation

• 3 Nash equilibrium

• 3.1 Examples of differences between Nash equilibria and ESSes

• 4 Vs. evolutionarily stable state

• 5 Stochastic ESS

• 6 Prisoner's dilemma

• 7 Human behavior

• 8 See also

• 9 References

• 10 Further reading

• 11 External links

History[edit]

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 in a book of essays titled On Evolution.[1] The 1972 essay is sometimes cited instead of the 1973 paper, but university libraries are much more likely to have copies of Nature. Papers in Nature are usually short; in 1974, Maynard Smith published a longer paper in the Journal of Theoretical Biology.[3] Maynard Smith explains further in his 1982 book Evolution and the Theory of Games.[4] Sometimes these are cited instead. In fact, the ESS has become so central to game theory that often no citation is given, as the reader is assumed to be familiar with it.

Maynard Smith mathematically formalised a verbal argument made by Price, which he read while peer-reviewing Price's paper. When Maynard Smith realized that the somewhat disorganised Price was not ready to revise his article for publication, he offered to add Price as co-author.

The concept was derived from R. H. MacArthur[5] and W. D. Hamilton's[6] work on sex ratios, derived from Fisher's principle, especially Hamilton's (1967) concept of an unbeatable strategy. Maynard Smith was jointly awarded the 1999 Crafoord Prize for his development of the concept of evolutionarily stable strategies and the application of game theory to the evolution of behaviour.[7]

Uses of ESS:

• The ESS was a major element used to analyze evolution in Richard Dawkins' bestselling 1976 book The Selfish Gene.

• The ESS was first used in the social sciences by Robert Axelrod in his 1984 book The Evolution of Cooperation. Since then, it has been widely used in the social sciences, including anthropology, economics, philosophy, and political science.

• In the social sciences, the primary interest is not in an ESS as the end of biological evolution, but as an end point in cultural evolution or individual learning.[8]

• In evolutionary psychology, ESS is used primarily as a model for human biological evolution.

Motivation[edit]

The Nash equilibrium is the traditional solution concept in game theory. It depends on the cognitive abilities of the players. It is assumed that players are aware of the structure of the game and consciously try to predict the moves of their opponents and to maximize their own payoffs. In addition, it is presumed that all the players know this (see common knowledge). These assumptions are then used to explain why players choose Nash equilibrium strategies.

Evolutionarily stable strategies are motivated entirely differently. Here, it is presumed that the players' strategies are biologically encoded and heritable. Individuals have no control over their strategy and need not be aware of the game. They reproduce and are subject to the forces of natural selection, with the payoffs of the game representing reproductive success (biological fitness). It is imagined that alternative strategies of the game occasionally occur, via a process like mutation. To be an ESS, a strategy must be resistant to these alternatives.

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 some Nash equilibria are not ESSes.