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Is deliberative self-control necessary to reign in selfish impulses, or does rational self-interest restrain the intuitive desire to cooperate? To answer this question, we introduce dual-process cognition into a formal game theoretic model of the evolution of cooperation. Agents play a mix of 1-shot and repeated Prisoner’s Dilemmas. They can either use “intuition”, which is not sensitive to game type, or pay a cost to “deliberate” and thereby tailor their strategy to the type of game they are facing. We find that selection favors one of two strategies: (i) intuitive defectors who never deliberate or (ii) dual-process agents that intuitively cooperate but sometimes use deliberation to defect in 1-shot games. Critically, evolution never favors agents that use deliberation to override selfish impulses: deliberation only serves to undermine cooperation. Thus, for the first time, we provide a clear ultimate-level explanation about why people may be intuitively cooperative, but reflectively greedy.