Evolutionarily stable sets in mixed-strategist models (Q1061651)

Evolutionary stable sets are used as an extension of the concept of an evolutionarily stable strategy (ESS). They have, as sets, essentially the same properties as ordinary ESSs. Here, ES sets are applied to the characterization of what will happen in an asexual population of mixed- strategists under frequency-dependent selection. Such a population will tend to establish some state, usually not a unique one, that belongs to an ES set. For an important class of widely used mixed-strategist models, ES sets are found to comprise just those population states that allow the possible behavioural acts to be equally successful, or, to put it more precisely, that establish an evolutionarily stable population strategy.