DETECTING ALL EVOLUTIONARILY STABLE STRATEGIES

In evolutionary game theory, the central solution concept is the evolutionarily stable state, which also can be interpreted as an evolutionarily stable population strategy (ESS). As such, this notion is a refinement of the Nash equilibrium concept in that it requires an additional stability property. In the present paper, an algorithm for detecting all ESSs of a given evolutionary game consisting of pairwise conflicts is presented which both is efficient and complete, since it involves a procedure avoiding the search for unstable equilibria to a considerable extent, and also has a finite, exact routine to check evolutionary stability of a given equilibrium. The article also contains the generalization of these results to the playing-the-field setting, where the payoff is nonlinear.