Noncooperative farsighted stable set in an n-player prisoners' dilemma

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 farsighted enough 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. By constructing a purely noncooperative farsighted stable set concretely, we prove its existence and uniqueness; further, we show that it supports the “all-defection” outcome as well as at least one Pareto-efficient outcome, which may or may not be the “all-cooperation” outcome. ∗The author is very grateful to Professor Eiichi Miyagawa for his insightful comments. He also acknowledges financial supports from Japan Society for the Promotion of Science (Grant-in-Aid for Scientific Research (C), No. 18530175). Address for correspondence: Noritsugu Nakanishi, Graduate School of Economics, Kobe University, Rokkodai-cho 2-1, Nada-ku, Kobe 657-8501, JAPAN. Tel: +78-803-6837 (Office Direct). Fax: +78-803-7293 (Faculty Office). E-mail: [email protected] †Printed: July 24, 2007 (ver. 1, Nov. 2006; ver. 2, Jan. 2007).