The Limits of Reciprocity

Abstract

Besides meeting the Nash condition (Axelrod's so-called “collective stability”), an evolutionary equilibrium must be an attractor—either an evolutionary equilibrium point (EEP) or an evolutionary equilibrium region (EER). In this analysis of Prisoners' Dilemma and Chicken environments, the “archetype” strategies (COOPERATE and DEFECT in Prisoners' Dilemma and COWARD and DAREDEVIL in Chicken) were augmented by the “reactive” strategies TIT FOR TAT and BULLY—entering separately in 3 x 3 interactions and jointly in 4 x 4 interactions. An instant-response assumption was employed that stacked the deck somewhat in favor of TIT FOR TAT. Nevertheless, in no case was all-TIT FOR TAT ever an EEP, although some conditions generated a mixed EER with only “nice” behaviors represented. A credible model should imply an equilibrium in which both “mean” and “nice” behaviors are represented. Remarkably, none of the conditions postulated here led to such an outcome. This unsatisfying result suggests the importance of introducing a PUNISHER strategy as described elsewhere by the authors.