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Equal Loss under Separatorization and Egalitarian Values

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  • Zhengxing Zou

    (Vrije Universiteit Amsterdam)

  • Rene van den Brink

    (Vrije Universiteit Amsterdam)

Abstract

We characterize the equal division value, the equal surplus division value, and the class of their ane combinations for TU-games involving equal loss under separatorization. This axiom requires that, if a player becomes a dummifying player (Casajus and Huettner, in Economics Letters 122(2): 167-169, 2014), then any two other players are equally affected.

Suggested Citation

  • Zhengxing Zou & Rene van den Brink, 2020. "Equal Loss under Separatorization and Egalitarian Values," Tinbergen Institute Discussion Papers 20-043/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20200043
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    References listed on IDEAS

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    1. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(3), pages 309-319.
    2. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2016. "Axiomatic characterizations under players nullification," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 47-57.
    3. Takumi Kongo, 2018. "Effects of Players’ Nullification and Equal (Surplus) Division Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 20(01), pages 1-14, March.
    4. van den Brink, Rene, 2007. "Null or nullifying players: The difference between the Shapley value and equal division solutions," Journal of Economic Theory, Elsevier, vol. 136(1), pages 767-775, September.
    5. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    6. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    7. René Brink & Yukihiko Funaki, 2009. "Axiomatizations of a Class of Equal Surplus Sharing Solutions for TU-Games," Theory and Decision, Springer, vol. 67(3), pages 303-340, September.
    8. Kongo, Takumi, 2019. "Players’ nullification and the weighted (surplus) division values," Economics Letters, Elsevier, vol. 183(C), pages 1-1.
    9. Casajus, André & Huettner, Frank, 2014. "Null, nullifying, or dummifying players: The difference between the Shapley value, the equal division value, and the equal surplus division value," Economics Letters, Elsevier, vol. 122(2), pages 167-169.
    10. Casajus, André & Huettner, Frank, 2014. "Weakly monotonic solutions for cooperative games," Journal of Economic Theory, Elsevier, vol. 154(C), pages 162-172.
    11. Takumi Kongo, 2020. "Similarities in axiomatizations: equal surplus division value and first-price auctions," Review of Economic Design, Springer;Society for Economic Design, vol. 24(3), pages 199-213, December.
    12. Koji Yokote & Yukihiko Funaki, 2017. "Monotonicity implies linearity: characterizations of convex combinations of solutions to cooperative games," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(1), pages 171-203, June.
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    Cited by:

    1. Zhang, Li & Xu, Genjiu & Sun, Hao & Li, Wenzhong, 2023. "Players’ dummification and the dummified egalitarian non-separable contribution value," Economics Letters, Elsevier, vol. 226(C).
    2. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).

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    More about this item

    Keywords

    Cooperative game; equal division value; equal surplus division value; axiomatization;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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