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Axiomatizations of Coalition Aggregation Functions

Author

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  • Takaaki Abe

    (School of Political Science and Economics, Waseda University)

Abstract

We axiomatize Hart and Kurz's (1983) two coalition aggregation functions known as the γfunction and the δ-function. A coalition aggregation function is a mapping that assigns a partition to each coalition profile, where a coalition profile is a vector of coalitions selected by all players. Through our axiomatization results, we observe that neither the γ-function nor the δ-function satisfies monotonicity. We propose a monotonic function and axiomatically characterize it. An impossibility result on monotonicity is also provided.

Suggested Citation

  • Takaaki Abe, 2019. "Axiomatizations of Coalition Aggregation Functions," Working Papers 1904, Waseda University, Faculty of Political Science and Economics.
    • Handle: RePEc:wap:wpaper:1904
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    References listed on IDEAS

    as
    1. Koczy, Laszlo A. & Lauwers, Luc, 2004. "The coalition structure core is accessible," Games and Economic Behavior, Elsevier, vol. 48(1), pages 86-93, July.
    2. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
    3. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    4. Takaaki Abe, 2018. "Stable coalition structures in symmetric majority games: a coincidence between myopia and farsightedness," Theory and Decision, Springer, vol. 85(3), pages 353-374, October.
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    More about this item

    Keywords

    axiomatization; coalition formation; coalition structure; monotonicity;
    All these keywords.

    JEL classification:

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

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