EVOLUTIONARY SELECTION AGAINST DOMINATED STRATEGIES

A class of evolutionary selection dynamics is defined, and the definin g property convex monotonicity. is shown to be sufficient and essentia lly necessary for the elimination of strictly dominated pure strategie s. More precisely: (1) all strictly dominated strategies :Ire eliminat ed along all interior solutions in all convex monotonic dynamics. and (2) for all selection dynamics where the pure-strategy growth rates ar e functions of their current payoffs, violation of convex monotonicity implies that there exist games with strictly dominated strategies tha t survive along a large set of interior solutions. The class of convex monotonic dynamics is shown to contain certain selection dynamics tha t arise in models of social evolution by way of imitation. (C) 1996 Ac ademic Press, Inc.