Effects of asynchronism on evolutionary games

We analyze the influence of the update dynamics on symmetric 2-player evolutionary games, which are among the most used tools to study the emergence of cooperation in populations of interacting agents. A synchronous dynamics means that, at each time step, all the agents of the population update their strategies simultaneously. An extreme case of asynchronism is sequential dynamics, in which only one agent is updated each time. We first show that these two opposite update dynamics can lead to very different outcomes and that sequential dynamics is detrimental to the emergence of cooperation only when the probability of imitating the most successful neighbors is high. In this sense, we can say that, when the update dynamics has some influence, in general asynchronism is beneficial to the emergence of cooperation. We then explore the consequences of using intermediate levels of asynchronism, where only a fraction of the agents update their behavior each time. In general, the level of cooperation changes smoothly and monotonically as we gradually go from synchronous to sequential dynamics. However, there are some exceptions that should be taken into account. In addition, the results show that the possibility of agents taking irrational decisions has a key role in the sensitivity of these models to changes in the update dynamics. Explanations for the observed behaviors are advanced.