This paper investigates a deterministic evolutionary process governing the adoption of strategies for playing the repeated Prisoners' Dilemma. Agents playing unsuccessful strategies attempt to imitate the strategies of successful agents. Because agents' strategies are unobservable, they must be inferred from a memory of pairwise play and a knowledge of the strategy space. As a result, winning strategies can be confused with other, inferior strategies, and this imperfect imitation can enhance the growth (or slow the decline) of under-performing strategies. In contrast to results obtained under payoff-monotonic dynamics such as the replicator dynamic or an analysis of Neutrally Stable Strategies, cooperation is eliminated in the long run; agents' inability to observe the strategies of successful players can fundamentally change the evolutionary dynamics.
Imitation dynamics in the repeated Prisoners' Dilemma: An exploratory example