Asynchronous Stochastic Dynamics and the Spatial Prisoner’s Dilemma Game

Abstract

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.

Update Dynamics, Strategy Exchanges and the Evolution of Cooperation in the Snowdrift Game

“…When this game is played using the proportional rule (see Section 2) it was found that sequential updating favors cooperation [13]. In our work with both games [2][3] [5] we confirmed the results of previous works but also found that asynchronous updating is detrimental for cooperation for very small noise values only, especially for regular networks. We also showed that the influence of the update dynamics depends mainly on the noise present in the strategy update process [4]: asynchronism becomes increasingly beneficial to cooperators as the noise level grows up to a certain value.…”

Instability in Spatial Evolutionary Games

“…SFNs have a power law degree distribution P (k) ∼ k −γ that is also very common in real social networks 3 . SFNs are built in the following way: the network is initialized with m fully connected nodes.…”

“…The influence of the update dynamics is addressed, for example, in [8] and [9]. We also studied the influence of the update dynamics and found that, in general an asynchronous dynamics supports more cooperators than a synchronous one [3,4,5,6].…”

Examples of Fast and Slow Convergence of 2D Asynchronous Cellular Systems

“…To what extent does a random updating scheme change qualitative properties of a given system? For the sake of conciseness, we refer to [3,6] for a review of works related to asynchronism and for a discussion on updating schemes. The different types of convergence we exhibit, from very fast to very slow, seem to confirm that the updating scheme is an important factor to understand the evolution of a cellular automaton.…”