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A Minimal Test for Convex Games and the Shapley Value

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Author Info

  • Voorneveld, Mark

    (CentER and Department of Econometrics)

  • Grahn, Sofia

    (Department of Economics)

Abstract

A set of necessary and sufficient conditions for convexity of a transferable utility game in terms of its decomposition into unanimity games is shown to be minimal: none of the conditions is redundant. The result is used to provide an axiomatization of the Shapley value on the set of convex games.

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Bibliographic Info

Paper provided by Uppsala University, Department of Economics in its series Working Paper Series with number 2001:2.

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Length: 8 pages
Date of creation: 01 Feb 2001
Date of revision:
Handle: RePEc:hhs:uunewp:2001_002

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Postal: Department of Economics, Uppsala University, P. O. Box 513, SE-751 20 Uppsala, Sweden
Phone: + 46 18 471 25 00
Fax: + 46 18 471 14 78
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Web page: http://www.nek.uu.se/
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Keywords: Convex game; unanimity game; Shapley value; axiomatization;

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  1. 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.
  2. Curiel, I. & Pederzoli, G. & Tijs, S.H., 1989. "Sequencing games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154243, Tilburg University.
  3. O'Neill, Barry, 1982. "A problem of rights arbitration from the Talmud," Mathematical Social Sciences, Elsevier, vol. 2(4), pages 345-371, June.
  4. Judith Timmer & Peter Borm & Stef Tijs, 2004. "On three Shapley-like solutions for cooperative games with random payoffs," International Journal of Game Theory, Springer, vol. 32(4), pages 595-613, 08.
  5. Curiel, Imma & Pederzoli, Giorgio & Tijs, Stef, 1989. "Sequencing games," European Journal of Operational Research, Elsevier, vol. 40(3), pages 344-351, June.
  6. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
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