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Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results

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  • Pedro Calleja

    (Universitat de Barcelona)

  • Francesc Llerena

    (Universitat Rovira i Virgili, CREIP)

Abstract

On the domain of cooperative games with transferable utility, we investigate if there are single-valued solutions that reconcile individual rationality, core selection, consistency and monotonicity (with respect to the worth of the grand coalition). This paper states some impossibility results for the combination of core selection with either complement consistency (Moulin, J Econ Theory 36:120–148, 1985) or projected consistency (Funaki, Dual axiomatizations of solutions of cooperative games. Mimeo, Tokyo, 1998), and core selection, max consistency (Davis and Maschler, Naval Res Logist Q 12:223–259, 1965) and monotonicity. By contrast, possibility results are manifest when combining individual rationality, projected consistency and monotonicity.

Suggested Citation

  • Pedro Calleja & Francesc Llerena, 2017. "Rationality, aggregate monotonicity and consistency in cooperative games: some (im)possibility results," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 48(1), pages 197-220, January.
    • Handle: RePEc:spr:sochwe:v:48:y:2017:i:1:d:10.1007_s00355-016-0966-z
    DOI: 10.1007/s00355-016-0966-z
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    Cited by:

    1. Zhengxing Zou & Rene van den Brink & Yukihiko Funaki, 2020. "Compromising between the proportional and equal division values: axiomatization, consistency and implementation," Tinbergen Institute Discussion Papers 20-054/II, Tinbergen Institute.
    2. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    3. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    4. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
    5. Bergantiños, Gustavo & Moreno-Ternero, Juan D., 2022. "Monotonicity in sharing the revenues from broadcasting sports leagues," European Journal of Operational Research, Elsevier, vol. 297(1), pages 338-346.
    6. Calleja, Pedro & Llerena, Francesc & Sudhölter, Peter, 2018. "Monotonicity and weighted prenucleoli: A characterization without consistency," Discussion Papers on Economics 4/2018, University of Southern Denmark, Department of Economics.
    7. Pedro Calleja & Francesc Llerena & Peter Sudhölter, 2020. "Monotonicity and Weighted Prenucleoli: A Characterization Without Consistency," Mathematics of Operations Research, INFORMS, vol. 45(3), pages 1056-1068, August.
    8. Zhengxing Zou & René Brink & Yukihiko Funaki, 2022. "Sharing the surplus and proportional values," Theory and Decision, Springer, vol. 93(1), pages 185-217, July.

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