Evolution of cooperation in two-level Prisoner's Dilemma

We consider continuous Prisoner's Dilemma played in spatial setting by group-structured populations. The population dynamics consists of individual-level birth and death and group-level fission and extinction events. Each individual plays games with all other individuals within their group, while groups play games against their nearest neighbours. Payoffs from individual-level games affect birth rates of individuals, and payoffs from group-level games affect group extinction and fission probabilities. We show that a certain level of cooperation is maintained due to specific between-group dynamics even though the within-group evolution by itself always results in a complete loss of cooperation. The spatial nature of games and resulting fissioning and extinction events is essential for the evolution of cooperation: without it cooperation is never maintained. Analyzing various scenarios of between-group fission and extinction events, we find that higher levels of cooperation evolve when the selection affecting fission and extinction events is local rather than global.