Simple evolution drives direct reciprocity to maximum payoff in social dilemmas

Abstract

Direct reciprocity is a mechanism for evolution of cooperation based on repeated interactions between the same individuals. Direct reciprocity can help natural selection to favor cooperators over defectors, but whether or not cooperation prevails depends on the details of the evolutionary dynamics. We describe simple processes of evolution that have the astonishing ability of driving direct reciprocity to maximum payoff in all social dilemmas which we study. The basic process is based on mutation and pairwise comparison. Mutation samples strategies near the boundary of the strategy space. Pairwise comparison includes a parameter for intensity of selection. For large population sizes, intermediate to high mutation rates and intermediate to strong intensities of selection, we find that the process leads to communities of strategies that reach maximum payoff in Prisoner's Dilemma, Snowdrift, Stag Hunt and Harmony games. Maximum payoff in all four games is consistently achieved if players have access to memory-2 strategies. Memory-1 strategies have the capacity to resolve all four social dilemmas, but they are usually defeated by a ``Hold-trap'' in Snowdrift games.