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Cooperation in Repeated Games When the Number of Stages is not Commonly Known
Abraham Neyman
Abstract
It is shown that an exponentially small departure from the common knowledge assumption on the number T of repetitions of the prisoners’ dilemma already enables cooperation. More generally, with such a departure, any feasible individually rational outcome of any one-shot game can be approximated by a subgame perfect equilibrium of a finitely repeated version of that game. The sense in which the departure from common knowledge is small is as follows: (I) With probability one, the players know T with precision ±K. (ii) With probability 1 − s, the players know T precisely; moreover, this knowledge is mutual of order sT. (iii) The deviation of T from its finite expectation is exponentially small.
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