Evolution of direct reciprocity in group-structured populations

TL;DR

This paper investigates how group structure influences the evolution of reciprocal cooperation, revealing that its effect varies with the benefit of cooperation and the population's interaction dynamics.

Contribution

It provides a game-theoretic analysis of cooperation in group-structured populations, considering different time-scale scenarios and their impact on cooperation levels.

Findings

Group structure enhances cooperation when benefits are small.

Well-mixed populations promote more cooperation when benefits are large.

The effect of population structure depends on the benefit of cooperation.

Abstract

People tend to have their social interactions with members of their own community. Such group-structured interactions can have a profound impact on the behaviors that evolve. Group structure affects the way people cooperate, and how they reciprocate each other's cooperative actions. Past work has shown that population structure and reciprocity can both promote the evolution of cooperation. Yet the impact of these mechanisms has been typically studied in isolation. In this work, we study how the two mechanisms interact. Using a game-theoretic model, we explore how people engage in reciprocal cooperation in group-structured populations, compared to well-mixed populations of equal size. To derive analytical results, we focus on two scenarios. In the first scenario, we assume a complete separation of time scales. Mutations are rare compared to between-group comparisons, which themselves are rare compared to within-group comparisons. In the second scenario, there is a partial separation of time scales, where mutations and between-group comparisons occur at a comparable rate. In both scenarios, we find that the effect of population structure depends on the benefit of cooperation. When this benefit is small, group-structured populations are more cooperative. But when the benefit is large, well-mixed populations result in more cooperation. Overall, our results reveal how group structure can sometimes enhance and sometimes suppress the evolution of cooperation.