Behavior-dependent contexts for repeated plays of the Prisoner's Dilemma II: Dynamical aspects of the evolution of cooperation

Iterated Prisoner's Dilemma models are proposed in which, at any trial, the probability of staying in the game depends on the outcome of the previous trial. If a player's choice depends on its own play (cooperate or defect) at the previous trial, it becomes possible for cooperative strategies to increase when rare in a population of egoists. A dynamic analysis is used to demonstrate that stable polymorphisms may result, and may involve more strategies than just Tit-for-Tat and all-Defect. The tendency for clustering among like strategists to enhance their initial increase when rare is also explored dynamically.