The Evolutionary Stability of Cooperation in the Iterated Prisoner's Dilemma

We establish conditions under which cooperation will evolve in conflict situations modelled as tournaments of iterated Prisoner’s Dilemma games. Though no strategies that are less than half of the population turn out to be stable even in the weakest sense, a majority condition ensures stability of nice (never the first to defect) and retaliatory (defect immediately in response to partner’s defection) strategies when the ‘shadow of the future’ is sufficiently long. Axelrod’s simulation findings are fully supported in that all nice and retaliatory strategies prove to be evolutionarily stable once in the majority, leading to the unique stable state of the population-universal cooperation.