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The stable set of the social conflict game with commitments: existence, uniqueness, and efficiency

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  • Toshiyuki Hirai

    (University of Toyama)

Abstract

We investigate the stable sets of social conflict games by employing the framework of the (abstract) system by Greenberg (Theory of social situations: an alternative game theoretic approach. Cambridge University Press, Cambridge, 1990). The social conflict game is a class of strategic games that includes the prisoners’ dilemma and the chicken game. We first show that the stable set generally fails to exist in a system that is directly derived from the social conflict game. In this system, the stable set exists if and only if the strong equilibrium exists in the underlying game. If the stable set exists, it coincides with the set of the strong equilibria that is equivalent to the core for the system. Then, we turn to a modified system where the players are allowed to make commitments. In the system with commitments, the stable set always exists, and it consists of efficient outcomes with a certain property. We also discuss the relationship between the core and the stable set for the system with commitments.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jogath:v:46:y:2017:i:1:d:10.1007_s00182-016-0527-9
    DOI: 10.1007/s00182-016-0527-9
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    References listed on IDEAS

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    1. Akira Okada, 2000. "The Efficiency Principle in Non-Cooperative Coalitional Bargaining," The Japanese Economic Review, Japanese Economic Association, vol. 51(1), pages 34-50, March.
    2. Saijo, Tatsuyoshi & Yamato, Takehiko, 1999. "A Voluntary Participation Game with a Non-excludable Public Good," Journal of Economic Theory, Elsevier, vol. 84(2), pages 227-242, February.
    3. Armando Gomes, 2005. "Multilateral Contracting with Externalities," Econometrica, Econometric Society, vol. 73(4), pages 1329-1350, July.
    4. Effrosyni Diamantoudi, 2005. "Stable cartels revisited," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 26(4), pages 907-921, November.
    5. Yoshio Kamijo & Shigeo Muto, 2010. "Farsighted Coalitional Stability Of A Price Leadership Cartel," The Japanese Economic Review, Japanese Economic Association, vol. 61(4), pages 455-465, December.
    6. 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.
    7. Noritsugu Nakanishi, 2009. "Noncooperative farsighted stable set in an n-player prisoners’ dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(2), pages 249-261, June.
    8. Greenberg, Joseph, 1989. "Deriving strong and coalition-proof nash equilibria from an abstract system," Journal of Economic Theory, Elsevier, vol. 49(1), pages 195-202, October.
    9. Okada, Akira, 1993. "The Possibility of Cooperation in an n-Person Prisoners' Dilemma with Institutional Arrangements," Public Choice, Springer, vol. 77(3), pages 629-656, November.
    10. Akihiro Suzuki & Shigeo Muto, 2005. "Farsighted Stability in an n-Person Prisoner’s Dilemma," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 431-445, September.
    11. Claude d'Aspremont & Alexis Jacquemin & Jean Jaskold Gabszewicz & John A. Weymark, 1983. "On the Stability of Collusive Price Leadership," Canadian Journal of Economics, Canadian Economics Association, vol. 16(1), pages 17-25, February.
    12. Kyle Hyndman & Debraj Ray, 2007. "Coalition Formation with Binding Agreements," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(4), pages 1125-1147.
    13. Ryusuke Shinohara, 2010. "Coalition-proof equilibria in a voluntary participation game," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(4), pages 603-615, October.
    14. Daniel J. Seidmann & Eyal Winter, 1998. "A Theory of Gradual Coalition Formation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 65(4), pages 793-815.
    15. Daniel G. Arce M., 1994. "Stability Criteria for Social Norms with Applications to the Prisoner's Dilemma," Journal of Conflict Resolution, Peace Science Society (International), vol. 38(4), pages 749-765, December.
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    Cited by:

    1. 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.

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    More about this item

    Keywords

    Social conflict game; (abstract) system; Theory of social situations; Stable set; Commitment;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D74 - Microeconomics - - Analysis of Collective Decision-Making - - - Conflict; Conflict Resolution; Alliances; Revolutions

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