"An ESS or evolutionarily stable strategy is a strategy such that, if all the members of a population adopt it, no mutant strategy can invade." --Maynard Smith (1982).
Evolutionarily stable states are frequently used to identify solutions to the replicator equation, given in its linear payoff form by
This is similar but distinct from the concept of an evolutionarily stable strategy.
It can be shown that for the replicator equation if a state is evolutionarily stable then it is an asymptotically stable rest point, so the evolutionarily stable states are often taken as solutions of the replicator equation. The converse is true if the game matrix is symmetric.
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