Network Regularity and the Influence of Asynchronism on the Evolution of Cooperation

In a population of interacting agents, the update dynamics defines the temporal relation between the moments at which agents update the strategies they use when they interact with other agents. The update dynamics is said to be synchronous if this process occurs simultaneously for all the agents and asynchronous if this is not the case. On the other hand, the network of contacts defines who may interact with whom. In this paper, we investigate the features of the network of contacts that play an important role in the influence of the update dynamics on the evolution of cooperative behaviors in a population of agents. First we show that asynchronous dynamics is detrimental to cooperation only when 1) the network of contacts is highly regular and 2) there is no noise in the strategy update process. We then show that, among the different features of the network of contacts, network regularity plays indeed a major role in the influence of the update dynamics, in combination with the temporal scale at which clusters of cooperator agents grow.