Abstract
Axelrod found TIT-FOR-TAT to be a highly successful strategy in the Prisoners' Dilemma payoff environment. He concluded that a natural selection process in favor of TIT-FOR-TAT explains the evolutionary emergence of cooperation. This article shows that, contrary to Axelrod, TIT-FOR-TAT does not approach 100% fixation in the population. More generally, TIT-FOR-TAT is not a robustly successful strategy if Axelrod's exact assumptions do not apply—for example, if there is a cost of complexity or a probability of error, or when players compete in an elimination contest rather than a round-robin tournament. In fact, it is unreasonable to expect any single strategy to win out in evolutionary competition. Constructively, we show that the presence of a PUNISHER strategy typically generates, consistent with observation, an interior equilibrium in which more and less cooperative strategies simultaneously coexist.
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