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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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    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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