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Axiomatizations of coalition aggregation functions

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  • Abe, Takaaki

Abstract

We axiomatize Hart and Kurz’s (1983) two coalition aggregation functions known as the γ-function and the δ-function. A coalition aggregation function is a mapping that assigns a partition to each profile of coalitions selected by 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.

Suggested Citation

  • Abe, Takaaki, 2020. "Axiomatizations of coalition aggregation functions," Mathematical Social Sciences, Elsevier, vol. 103(C), pages 69-75.
    • Handle: RePEc:eee:matsoc:v:103:y:2020:i:c:p:69-75
    DOI: 10.1016/j.mathsocsci.2019.12.001
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    References listed on IDEAS

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    1. Casajus, André, 2009. "Outside options, component efficiency, and stability," Games and Economic Behavior, Elsevier, vol. 65(1), pages 49-61, January.
    2. Bogomolnaia, Anna & Jackson, Matthew O., 2002. "The Stability of Hedonic Coalition Structures," Games and Economic Behavior, Elsevier, vol. 38(2), pages 201-230, February.
    3. 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.
    4. Gallo, Oihane & Inarra, Elena, 2018. "Rationing rules and stable coalition structures," Theoretical Economics, Econometric Society, vol. 13(3), September.
    5. Hart, Sergiu & Kurz, Mordecai, 1983. "Endogenous Formation of Coalitions," Econometrica, Econometric Society, vol. 51(4), pages 1047-1064, July.
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