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Cooperation in Repeated Games When the Number of Stages is not Commonly Known
Author(s) -
Neyman Abraham
Publication year - 1999
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.1111/1468-0262.00003
Subject(s) - mathematical economics , repeated game , economics , mathematics , game theory
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 − ε , the players know T precisely; moreover, this knowledge is mutual of order ε T . (iii) The deviation of T from its finite expectation is exponentially small.