Evolutionary Selection against Dominated Strategies

A class of evolutionary selection dynamics is defined, and the defining property, convex monotonicity, is shown to be sufficient and essentially necessary for the elimination of strictly dominated pure strategies. More precisely: (1) all strictly dominated strategies are eliminated along all interior solutions in all convex monotonic dynamics, and (2) for all selection dynamics where the pure-strategy growth rates are functions of their current payoffs, violation of convex monotonicity implies that there exist games with strictly dominated strategies that survive along a large set of interior solutions. The class of convex monotonic dynamics is shown to contain certain selection dynamics that arise in models of social evolution by way of imitation.