Cooperation in Repeated Games When the Number of Stages is not Commonly Known
Econometrica · 1999 · Volume 67 · Issue 1
Abstract
It is shown that an exponentially small departure from the common knowledge assumption on the numberTof 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 knowTwith precision ±K. (ii) With probability 1 −ε, the players knowTprecisely; moreover, this knowledge is mutual of orderεT. (iii) The deviation ofTfrom its finite expectation is exponentially small.
Keywords
Game theory, finitely repeated games, common knowledge, prisoners' dilemma, cooperation.
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