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On the existence and efficiency of the von Neumann-Morgenstern stable set in a n-player prisoners' dilemma


Author Info

  • Noritsugu Nakanishi

    (Graduate School of Economics, Kobe University, Rokkodai-cho 2-1, Nada-ku, Kobe 657-8501, JAPAN Final version June 2001)


We show that there exist von Neumann-Morgenstern (vN-M) stable sets in a n-player version of the prisoners' dilemma game with preplay negotiations in which every player can deviate unilaterally from the currently proposed combination of actions but can not do so jointly with other players, and that every vN-M stable set includes at least one Pareto-efficient outcome. The negotiation among the players is formulated as the "individual contingent threats situation" within the framework of the theory of social situations due to Greenberg (1990). The method of proving the existence also provides us with a step-by-step method of constructing the vN-M stable set.

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Bibliographic Info

Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 30 (2001)
Issue (Month): 2 ()
Pages: 291-307

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Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:291-307

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Related research

Keywords: Preplay negotiation · von Neumann-Morgenstern stable set · Prisoners' dilemma · Social situations · Pareto efficiency;

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Cited by:
  1. Inarra, Elena & Concepcion Larrea, M. & Saracho, Ana I., 2007. "The supercore for normal-form games," Journal of Economic Theory, Elsevier, vol. 132(1), pages 530-538, January.
    • Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & Saracho de la Torre, Ana Isabel, 2003. "The Supercore for Normal Form Games," IKERLANAK 2003-04, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
  2. Iñarra García, María Elena & Larrea Jaurrieta, María Concepción & Saracho de la Torre, Ana Isabel, 2012. "The von Neumann-Morgenstern stable sets for 2x2 games," IKERLANAK Ikerlanak;2012-65, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.


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