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Three steps ahead

Heller, Yuval (2012): Three steps ahead.

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We present an evolutionary model of a population interacting in repeated Prisoner's Dilemma. Each type is characterized by the number of steps he looks ahead, and each agent has an independent probability to observe the opponent's type. We show that if this probability is not too close to 0 or 1, then the evolutionary process admits a stable outcome, in which the population includes a mixture of “naive” agents who look 1 step ahead, and “moderately sophisticated” agents who look 3 steps ahead. Moreover, this outcome is unique under the additional assumption that agents present reciprocity at early stages of the interaction.

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