EVOLUTIONARY EQUILIBRIA - CHARACTERIZATION THEOREMS AND THEIR IMPLICATIONS

To understand the meaning of evolutionary equilibria, it is necessary to comprehend the ramifications of the evolutionary model. For instanc e, a full appreciation of Axelrod's The Evolution of Cooperation requi res that we identify assumptions under which conditionally cooperative strategies, like Tit For Tat, are and are not evolutionarily stable. And more generally, when does stability fail? To resolve these questio ns we re-examine the very foundations of the evolutionary model. The r esults of this paper can be analytically separated into three parts. T he first part is conceptual: it identifies the evolutionary model's as sumptions and shows how different assumptions imply different types of evolutionary stability. The second part is deductive: it establishes necessary and sufficient conditions for the types of evolutionary stab ility identified in the first part, and demonstrates in which games th ese kinds of stability can (and cannot) be attained. The third and fin al part is applied: it relates the general findings (which are indepen dent of the specific payoffs of any particular evolutionary game) to t he issue of the evolutionary stability of cooperation. Results on coop eration appear throughout the paper as they both exemplify and motivat e the general results. These results essentially explain when cooperat ion is and is not stable, and why, thus shedding new light on the mean ing and applicability of Axelrod's widely known claims.