The prisoner’s dilemma on co-evolving networks under perfect rationality

We consider the prisoner’s dilemma being played repeatedly on a dynamic network, where agents may choose their actions as well as their co-players. This leads to co-evolution of network structure and strategy patterns of the players. Individual decisions are made fully rationally and are based on local information only. They are made such that links to defecting agents are resolved and that cooperating agents build up new links. The exact form of the updating scheme is motivated by profit maximization and not by imitation. If players update their decisions in a synchronized way the system exhibits oscillatory dynamics: Periods of growing cooperation (and total linkage) alternate with periods of increasing defection. The cyclical behavior is reduced and the system stabilizes at significant total cooperation levels when players are less synchronized. In this regime we find emergent network structures resembling ‘complex’ and hierarchical topology. The exponent of the power-law degree distribution ( γ∼8.6) perfectly matches empirical results for human communication networks.