The evolution of cooperation based on indirect reciprocity and spatial locality in continuous space

How cooperation evolves despite its disadvantage to local selfishness has been a challenging theme for many years. Several mechanisms have been proposed, among which reputation-based indirect reciprocity and spatial locality are two of the majors. However, only a few studies about their interaction exist. Here, we considered an agent-based model in a two-dimensional continuous space where not only the game-based interaction but also the transmission of agents’ reputation take place based on the spatial locality. Agents have one of the following three strategies as their gene: always defect, always cooperate or discriminate based on the recipient’s reputation. We tested four assessment rules in indirect reciprocity: Shunning, Stern Judging, Image Scoring and Simple Standing. We found that without mobility, first, as the spatial locality gets weaker, the cooperation rate drops. Second, for cooperation to evolve from an all-defector environment, the cluster of discriminators is necessary. We added mobility so that an agent will get closer to the one who donated to her and far away from the one who defected against her. We found that if the movement duration is long enough, a higher cooperation rate could be promoted.