Evolutionarily stable strategy

Abstract: We consider a class of matrix games in which successful strategies are rewarded by high reproductive rates, so become more likely to participate in subsequent playings of the game. Thus, over time, the strategy mix should evolve to some type of optimal or stable state. Maynard Smith and Price (1973) have introduced the concept of ESS (evolutionarily stable strategy) to describe a stable state of the game. We attempt to model the dynamics of the game both in the continuous case, with a system of non-linear first-order differential equations, and in the discrete case, with a system of non-linear difference equations. Using this model, we look at the notions of stability and asymptotic behavior. Our notion of stable equilibrium for the continuous dynamic includes, but is somewhat more general than, the notion of ESS.

Abstract: theoretical framework, the concept of the mixed strategy has not been realized in nature, and alternative strategies are very rare. Recent findings suggest that almost all alternative reproductive phenotypes within the sexes are due to alternative tactics within a conditional strategy, and, as such, while the average fitnesses of the alternative phenotypes are unequal, the strategy is favoured in evolution. Proximate mechanisms that underlie alternative phenotypes may have many similarities with those operating between the sexes.