Evolutionary Dynamics of Cumulative Reciprocity in Complex Networks

Abstract

The spontaneous emergence of cooperation among self-interested individuals has been a fundamental scientific challenge. A recent study proposed the cumulative reciprocity strategy, which unilaterally enforces equal payoffs to resist exploitation by defectors while maintaining mutual cooperation with co-operators. While this strategy performs remarkably well in well-mixed populations, its performance in structured populations remains unclear. Here, we systematically investigate, through simulations, the evolutionary dynamics of populations composed of individuals adopting cumulative reciprocity and reactive strategies across various classic static networks, dynamic networks with edge-rewiring, and real-world networks. Our results reveal that introducing cumulative reciprocity leads to noticeable changes in the evolutionary dynamics of populations employing reactive strategies. Specifically, cumulative reciprocity replaces the traditional generous tit-for-tat strategy as an evolutionarily dominant strategy, thereby fostering stable cooperation. This conclusion holds for different network structures, densities, population sizes, and mutation mechanisms. When network structure co-evolves with strategies, cumulative reciprocity still retains evolutionary advantages, though the stability of its dominance depends on the specific edge-rewiring mechanism. This study deepens our understanding of how cumulative reciprocity evolves in complex networks and offers new insights into the evolutionary dynamics of populations with large-scale strategy sets in structured environments.

Keywords

Evolution of cooperation / reactive strategies / small-world networks / scale-free networks / dynamic networks

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