Strategies of the First Population

Here we characterize the winning strategies for the aggressive populations, i.e., the setting of the parameters which lead to the victory of the aggressive population starting from a favorable initial condition. The analysis is different for different parameter ranges. In particular, the case of equal fitness between the two populations boils down to constant strategies, but the general case is not exhausted by them. In any case, we prove that also in the general case the winning strategies can always be found among the “bang-bang” functions, i.e., piecewise constant functions with at most one jump.