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

Author

Listed:
  • Noritsugu Nakanishi

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

Abstract

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.

Suggested Citation

  • Noritsugu Nakanishi, 2001. "On the existence and efficiency of the von Neumann-Morgenstern stable set in a n-player prisoners' dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(2), pages 291-307.
    • Handle: RePEc:spr:jogath:v:30:y:2001:i:2:p:291-307
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    Citations

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    Cited by:

    1. 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 1576-1857, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    2. Bloch, Francis & van den Nouweland, Anne, 2021. "Myopic and farsighted stable sets in 2-player strategic-form games," Games and Economic Behavior, Elsevier, vol. 130(C), pages 663-683.
    3. 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.
    4. Inarra, E. & Larrea, C. & Saracho, A., 2014. "The von Neumann–Morgenstern stable sets for the mixed extension of 2×2 games," Economics Letters, Elsevier, vol. 125(1), pages 70-73.
    5. 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 info:eu-repo/grantAgreeme, Universidad del País Vasco - Departamento de Fundamentos del Análisis Económico I.
    6. Toshiyuki Hirai, 2017. "The stable set of the social conflict game with commitments: existence, uniqueness, and efficiency," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(1), pages 149-166, March.

    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C79 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Other
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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