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Order Monotonic Solutions for Generalized Characteristic Functions

Author

Listed:
  • René van den Brink

    (VU University Amsterdam)

  • Enrique González-Aranguena

    (Universidad Complutense de Madrid, Spain)

  • Conrado Manuel

    (Universidad Complutense de Madrid, Spain)

  • Mónica del Pozo

    (Universidad Carlos III de Madrid, Spain)

Abstract

This discussion paper resulted in a publication in the 'European Journal of Operational Research', 2014, 238, 786-796. Generalized characteristic functions extend characteristic functions of 'classical' TU-games by assigning a real number to every ordered coalition being a permutation of any subset of the player set. Such generalized characteristic functions can be applied when the earnings or costs of cooperation among a set of players depends on the order in which the players enter a coalition. In the literature, the two main solutions for generalized characteristic functions are the one of Nowak and Radzik (1994), shortly called NR-value, and the one introduced by Sanchez and Bergantinos (1997), shortly called SB-value. In this paper, we introduce the axiom of order monotonicity with respect to the order of the players in a unanimity coalition, requiring that players who enter earlier should get not more in the corresponding (ordered) unanimity game than players who enter later. We propose several classes of order monotonic solutions for generalized characteristic functions that contain the NR-value and SB-value as special (extreme) cases. We also provide axiomatizations of these classes.

Suggested Citation

  • René van den Brink & Enrique González-Aranguena & Conrado Manuel & Mónica del Pozo, 2013. "Order Monotonic Solutions for Generalized Characteristic Functions," Tinbergen Institute Discussion Papers 13-093/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20130093
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    3. Araya-Córdova, P.J. & Vásquez, Óscar C., 2018. "The disaster emergency unit scheduling problem to control wildfires," International Journal of Production Economics, Elsevier, vol. 200(C), pages 311-317.
    4. C. Manuel & D. Martín, 2021. "A value for communication situations with players having different bargaining abilities," Annals of Operations Research, Springer, vol. 301(1), pages 161-182, June.
    5. Zhengxing Zou & Qiang Zhang & Surajit Borkotokey & Xiaohui Yu, 2020. "The extended Shapley value for generalized cooperative games under precedence constraints," Operational Research, Springer, vol. 20(2), pages 899-925, June.

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    More about this item

    Keywords

    Cooperative TU-game; generalized characteristic function; order monotonicity;
    All these keywords.

    JEL classification:

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

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