Abstract
We examine an n-player prisoners’ dilemma game in which only individual deviations are allowed, while coalitional deviations (even non-binding ones) are not, and every player is assumed to be sufficiently farsighted to understand not only the direct outcome of his own deviation but also the ultimate outcome resulting from a chain of subsequent deviations by other players. We show that there exists a unique, noncooperative farsighted stable set (NFSS) and that it supports at least one (partially and/or fully) cooperative outcome, which is individually rational and Pareto-efficient. We provide a sufficient condition for full cooperation. Further, we discuss the relationship between NFSS and other “stable set” concepts such as the (myopic) von Neumann–Morgenstern stable set, Harsanyi (1974)’s strictly stable set, Chwe (1994)’s largest consistent set, and the cooperative farsighted stable set examined by Suzuki and Muto (2005).
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The author is very grateful to Professor Eiichi Miyagawa, the editor and the associate editor of this journal for their insightful comments and suggestions. He also acknowledges the financial support of Japan Society for the Promotion of Science [Grant-in-Aid for Scientific Research (C), No. 18530175].
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Nakanishi, N. Noncooperative farsighted stable set in an n-player prisoners’ dilemma. Int J Game Theory 38, 249–261 (2009). https://doi.org/10.1007/s00182-009-0152-y
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DOI: https://doi.org/10.1007/s00182-009-0152-y