Synchronous and Asynchronous Network Evolution in a Population of Stubborn Prisoners

We study by computer simulation a population of individuals playing the prisoner's dilemma game. Each player has an invariable strategy (cooperate or defect) but the network of relationships between players is allowed to change over time following simple rules based on players' degree of satisfaction. The population almost always reaches a stable state and we observe that, in the long run, cooperators tend to cluster together in order to maintain a high average payoff and to protect themselves from exploiting defectors. Thus network topology plays an important role even though strategies are not allowed to evolve. We investigated both synchronous and asynchronous network dynamics, observing that asynchronous update, in addition of being more reasonable in a social setting, induces system stability more often than the synchronous one.