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Games of threats

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  • Kohlberg, Elon
  • Neyman, Abraham

Abstract

A game of threats on a finite set of players, N, is a function d that assigns a real number to any coalition, S⊆N, such that d(S)=−d(N∖S). A game of threats is not necessarily a coalitional game as it may fail to satisfy the condition d(∅)=0. We show that analogs of the classic Shapley axioms for coalitional games determine a unique value for games of threats. This value assigns to each player an average of d(S) across all the coalitions that include the player. Games of threats arise naturally in value theory for strategic games, and may have applications in other branches of game theory.

Suggested Citation

  • Kohlberg, Elon & Neyman, Abraham, 2018. "Games of threats," Games and Economic Behavior, Elsevier, vol. 108(C), pages 139-145.
    • Handle: RePEc:eee:gamebe:v:108:y:2018:i:c:p:139-145
    DOI: 10.1016/j.geb.2017.10.018
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    1. Elon Kohlberg & Abraham Neyman, 2017. "Cooperative Strategic Games," Discussion Paper Series dp706, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.
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    Cited by:

    1. Wenna Wang & Rene van den Brink & Hao Sun & Genjiu Xu & Zhengxing Zou, "undated". "The alpha-constant-sum games," Tinbergen Institute Discussion Papers 19-022/II, Tinbergen Institute.
    2. Csóka, Péter & Illés, Ferenc & Solymosi, Tamás, 2022. "On the Shapley value of liability games," European Journal of Operational Research, Elsevier, vol. 300(1), pages 378-386.
    3. Wenna Wang & René van den Brink & Hao Sun & Genjiu Xu & Zhengxing Zou, 2022. "On $$\alpha $$ α -constant-sum games," International Journal of Game Theory, Springer;Game Theory Society, vol. 51(2), pages 279-291, June.

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    1. Elon Kohlberg & Abraham Neyman, 2017. "Games of Threats," Discussion Paper Series dp710, The Federmann Center for the Study of Rationality, the Hebrew University, Jerusalem.

    More about this item

    Keywords

    Shapley value; Coalitional game;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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