A Unified Framework of Direct and Indirect Reciprocity

Abstract

Direct and indirect reciprocity are key mechanisms for evolution of cooperation. Direct reciprocity means individuals use their own experience to decide whether to cooperate with another person. Indirect reciprocity means they also consider the experiences of others. Although the two mechanisms are intertwined, they are typically studied in isolation. Here, we introduce a mathematical framework that allows us to explore both kinds of reciprocity simultaneously. We show that the well-known strategy ‘Generous Tit-for-Tat’ of direct reciprocity has a natural analogue in indirect reciprocity, which we call ‘Generous Scoring’. With an equilibrium analysis, we characterize under which conditions either of the two strategies can maintain cooperation. With simulations, we additionally explore which kind of reciprocity evolves when members of a population engage in social learning to adapt to their environment. We find that indirect reciprocity evolves if any two individuals meet only occasionally, when information about others is reliable, and when strategy mutations are rare. Our results draw unexpected connections between direct and indirect reciprocity, while highlighting important differences regarding their evolvability.