Initial image-based approach may enhance direct reciprocity for cooperation evolution

The puzzle of how cooperation arises in social dilemmas has been a central question in evolutionary game theory. Traditional studies have delineated direct and indirect reciprocity as distinct avenues for fostering cooperative behavior. Direct reciprocity hinges on recurrent interactions with the same individual, whereas indirect reciprocity involves leveraging information about the conduct of other participants. This study investigates strategy evolution within the iterated Prisoner’s Dilemma framework, focusing on a finite population and utilizing a refined Moran process. We explore the effectiveness of various strategies for discriminators, considering both repeated encounters with identical partners and the availability of public action records, to facilitate the emergence of cooperation. Our analysis reveals that the order of the performances of discriminator strategies depends on the cost-to-benefit ratio of cooperation. Discriminators utilizing indirect information from initial encounters generally outperform others, except in cases where the benefits significantly surpass the costs, a condition under which the conventional Tit-for-Tat approach prevails.