Evolutionary Dynamics of Direct and Indirect Reciprocities With Directional Interactions

Reciprocity is a potent mechanism that drives cooperation within human societies. Direct reciprocity involves interacting with individuals, while indirect reciprocity is reliant on anticipated rewards from a third party rather than someone they have interacted with directly. Despite being closely intertwined, current research isolates these two mechanisms, with further division of indirect reciprocity into positive and negative based on the directionality of daily interactions. To capture the coevolution of direct and indirect reciprocities, this work has developed a simple yet comprehensive model, allowing individuals to choose among these reciprocities arbitrarily. A comprehensive equilibrium analysis discovers that the analogous strategy of negative indirect reciprocity, called negative scoring (NSCO), has a stronger control property than the well-known reciprocity strategies. Utilizing evolutionary simulations, we find that directionality can indeed promote the emergence of indirect reciprocity. Overall, our findings shed light on a novel passageway toward a universal theory of direct and indirect reciprocities.