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Smoothness, nullified equal loss property and equal division values

Author

Listed:
  • Sylvain Ferrières

    () (Université de Bourgogne Franche-Comté, CRESE)

Abstract

We provide characterizations of the equal division values and their convex mixtures, using a new axiom on a fixed player set based on player nullification which requires that if a player becomes null, then any two other players are equally affected. Meanwhile, we also present a global and useful framework which enables differential calculus within the space of values, allowing to smoothly implement other axioms.

Suggested Citation

  • Sylvain Ferrières, 2016. "Smoothness, nullified equal loss property and equal division values," Working Papers 2016-01, CRESE.
  • Handle: RePEc:crb:wpaper:2016-01
    as

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    File URL: http://crese.univ-fcomte.fr/WP-2016-01.pdf
    File Function: First version, 2016
    Download Restriction: no

    References listed on IDEAS

    as
    1. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2016. "Axiomatic characterizations under players nullification," Mathematical Social Sciences, Elsevier, vol. 80(C), pages 47-57.
    2. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
    3. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March.
    4. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2015. "Preserving or removing special players: What keeps your payoff unchanged in TU-games?," Mathematical Social Sciences, Elsevier, vol. 73(C), pages 23-31.
    5. 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.
    6. Debreu, Gerard, 1972. "Smooth Preferences," Econometrica, Econometric Society, vol. 40(4), pages 603-615, July.
    7. Sylvain Béal & André Casajus & Frank Huettner & Eric Rémila & Philippe Solal, 2016. "Characterizations of weighted and equal division values," Theory and Decision, Springer, vol. 80(4), pages 649-667, April.
    8. 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.
    9. William Thomson, 2007. "Cost allocation and airport problems," RCER Working Papers 537, University of Rochester - Center for Economic Research (RCER).
    10. Casajus, André & Hüttner, Frank, 2012. "Nullifying vs. dummifying players or nullified vs. dummified players: The difference between the equal division value and the equal surplus division value," Working Papers 110, University of Leipzig, Faculty of Economics and Management Science.
    11. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Player nullification; smoothness; equal division; equal surplus division;

    JEL classification:

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

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