Partial information, noise and network topology in 2x2 games with memory

We investigate the collective behaviour of a large number of agents with one step memory horizon in the framework of evolutionary game theory. A refinement of the imitation process for memory agents that we call partial imitation is compared to the commonly employed complete imitation procedure. We combine pairwise comparison and random exploration to show that the cooperation density may be greatly reduced due to the refined imitation process. Partial imitation also greatly changes the fate of the individual strategies. We show that the ubiquitous Tit-For-Tat strategy is difficult to be observed in its entirety by deterministic agents. Consequently it becomes a less popular strategy with partial imitation. The other two famous strategies Grim Trigger and Pavlov on the other hand become more popular with partial imitation. With its unique repair abilities Pavlov also turns out to be the dominating strategy for noisy players, who do not act in accordance with their strategy at all times. We further find that small variations in the payoff parameters of the games can greatly affect the equilibrium cooperation density and find several transitions in different regions of the payoff parameter space