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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 cally 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.

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We investigate the influence of the update dynamics on the evolution of cooperation. Three of the most studied games in this area are used: Prisoner's Dilemma, Snowdrift and the Stag Hunt. Previous studies with the Prisoner's Dilemma game reported that less cooperators survive with the asynchronous version of the game than with the synchronous one. On the other side, studies with the Snowdrift game are not conclusive about this subject. Based on simulations with these three games, played on different types of networks and using different levels of noise in the choice of the next strategy to be adopted by the agents, we conclude that, in general, an asynchronous dynamics favors the evolution of cooperation. Results concerning the monotonicity of these models and their sensitivity to small changes in the synchrony rate are also reported. This work is a contribution to a better understanding of the conditions under which cooperation can emerge and how different parameters may influence this emergence.

We argue that intermediate levels of asynchronism should be explored when one uses evolutionary games to model biological and sociological systems. Usually, only perfect synchronism and continuous asynchronism are used, assuming that it is enough to test the model under these two opposite update methods. We believe that biological and social systems lie somewhere between these two extremes and that we should inquire how the models used in these situations behave when the update method allows more than one element to be active at the same time but not necessarily all of them. Here, we use an update method called Asynchronous Stochastic Dynamics which allows us to explore intermediate levels of asynchronism and we apply it to the Spatial Prisoner's Dilemma game. We report some results concerning the way the system changes its behaviour as the synchrony rate of the update method varies.