A resident strategy is evolutionarily stable if every distinct mutant earns lower expected fitness when introduced at sufficiently small positive frequency. The upper bound on the frequency may depend on the mutant. In a finite symmetric matrix game, is the expected payoff, with the second argument representing the population strategy. Affineness in this argument yields the two-condition criterion for evolutionary stability. Every evolutionarily stable strategy is a symmetric Nash equilibrium, but a tied best response must also be strictly outperformed against its own mutant population. The Hawk-Dove game supplies an interior stable mixture despite equality of all payoffs against the resident mixture.
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An Evolutionarily Stable Strategy (ESS) is a concept from evolutionary game theory that describes a strategy that, if adopted by a majority of a population, cannot be invaded by any alternative strategy that is initially rare. The concept was first introduced by the biologist John Maynard Smith in the 1970s as a way to explain stable behavioral patterns in animal populations.