Adversarial Scheduling in Evolutionary Game Dynamics
  Consider a system in which players at nodes of an underlying graph G repeatedly play Prisoner's Dilemma against their neighbors. The players adapt their strategies based on the past behavior of their opponents by applying the so-called win-stay lose-shift strategy. This dynamics has been studied in (Kittock 94), (Dyer et al. 2002), (Mossel and Roch, 2006).   With random scheduling, starting from any initial configuration with high probability the system reaches the unique fixed point in which all players cooperate. This paper investigates the validity of this result under various classes of adversarial schedulers. Our results can be sumarized as follows:   1. An adversarial scheduler that can select both participants to the game can preclude the system from reaching the unique fixed point on most graph topologies. 2. A nonadaptive scheduler that is only allowed to choose one of the participants is no more powerful than a random scheduler. With this restriction even an adaptive scheduler is not significantly more powerful than the random scheduler, provided it is "reasonably fair".   The results exemplify the adversarial scheduling approach we propose as a foundational basis for the generative approach to social science (Epstein 2007). 
Gabriel Istrate, Madhav V. Marathe and S. S. Ravi