Grouping promotes both partnership and rivalry with long memory in direct reciprocity

Biological and social scientists have long been interested in understanding how to reconcile individual and collective interests in the iterated Prisoner’s Dilemma. Many effective strategies have been proposed, and they are often categorized into one of two classes, ‘partners’ and ‘rivals.’ More recently, another class, ‘friendly rivals,’ has been identified in longer-memory strategy spaces. Friendly rivals qualify as both partners and rivals: They fully cooperate with themselves, like partners, but never allow their co-players to earn higher payoffs, like rivals. Although they have appealing theoretical properties, it is unclear whether they would emerge in an evolving population because most previous works focus on the memory-one strategy space, where no friendly rival strategy exists. To investigate this issue, we have conducted evolutionary simulations in well-mixed and group-structured populations and compared the evolutionary dynamics between memory-one and longer-memory strategy spaces. In a well-mixed population, the memory length does not make a major difference, and the key factors are the population size and the benefit of cooperation. Friendly rivals play a minor role because being a partner or a rival is often good enough in a given environment. It is in a group-structured population that memory length makes a stark difference: When longer-memory strategies are available, friendly rivals become dominant, and the cooperation level nearly reaches a maximum, even when the benefit of cooperation is so low that cooperation would not be achieved in a well-mixed population. This result highlights the important interaction between group structure and memory lengths that drive the evolution of cooperation.Author summary: In the evolution of cooperation, to what extent is cognitive capacity essential? The social brain hypothesis argued that the brain size of primates has increased with the social group size to manage complex social interactions, e.g., to reciprocate cooperation and punish free riders. On the other hand, in the study of the repeated Prisoner’s Dilemma, it has been shown that simple strategies that remember only the previous round can unilaterally control the payoffs even against more sophisticated strategies having longer memories. Thus, it is not straightforward to answer the question of how the evolution of cooperation changes when players are accessible to more elaborate memory-demanding strategies. This paper studies this question through evolutionary simulations and found that longer memory strategies substantially change the picture when the population has an internal structure. This study thus suggests the joint impact between cognitive capacity and the population structure in the evolution of cooperation, although these have often been studied independently.