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On extensions of the core and the anticore of transferable utility games

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  • Derks, Jean

    ()
    (Department of Knowledge Engineering)

  • Peters, Hans

    ()
    (Department of Quantitative Economics)

  • Sudhölter, Peter

    ()
    (Department of Business and Economics)

Abstract

We consider several related set extensions of the core and the anticore of games with transferable utility. An efficient allocation is undominated if it cannot be improved, in a specific way, by sidepayments changing the allocation or the game. The set of all such allocations is called the undominated set, and we show that it consists of finitely many polytopes with a core-like structure. One of these polytopes is the L1-center, consisting of all efficient allocations that minimize the sum of the absolute values of the excesses. The excess Pareto optimal set contains the allocations that are Pareto optimal in the set obtained by ordering the sums of the absolute values of the excesses of coalitions and the absolute values of the excesses of their complements. The L1-center is contained in the excess Pareto optimal set, which in turn is contained in the undominated set. For three-person games all these sets coincide. These three sets also coincide with the core for balanced games and with the anticore for antibalanced games. We study properties of these sets and provide characterizations in terms of balanced collections of coalitions. We also propose a single-valued selection from the excess Pareto optimal set, the min-prenucleolus, which is defined as the prenucleolus of the minimum of a game and its dual.

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Bibliographic Info

Paper provided by Department of Business and Economics, University of Southern Denmark in its series Discussion Papers of Business and Economics with number 4/2012.

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Length: 28 pages
Date of creation: 06 Jan 2012
Date of revision:
Handle: RePEc:hhs:sdueko:2012_004

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Postal: Department of Business and Economics, University of Southern Denmark, Campusvej 55, DK-5230 Odense M, Denmark
Phone: 65 50 32 33
Fax: 65 50 32 37
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Web page: http://www.sdu.dk/ivoe
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Keywords: Transferable utility game; core; anticore; core extension; min-prenucleolus;

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References

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  1. BOSSERT, Walter & DERKS, Jean & PETERS, Hans, 2001. "Efficiency in Uncertain Cooperative Games," Cahiers de recherche 2001-14, Universite de Montreal, Departement de sciences economiques.
  2. Guni Orshan & Peter Sudhölter, 2010. "The positive core of a cooperative game," International Journal of Game Theory, Springer, vol. 39(1), pages 113-136, March.
  3. Peleg, B, 1986. "On the Reduced Game Property and Its Converse," International Journal of Game Theory, Springer, vol. 15(3), pages 187-200.
  4. Camelia Bejan & Juan Gómez, 2009. "Core extensions for non-balanced TU-games," International Journal of Game Theory, Springer, vol. 38(1), pages 3-16, March.
  5. Derks, Jean & Peters, Hans, 1998. "Orderings, excess functions, and the nucleolus," Mathematical Social Sciences, Elsevier, vol. 36(2), pages 175-182, September.
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Cited by:
  1. Michel Grabisch & Peter Sudhölter, 2014. "The positive core for games with precedence constraints," Documents de travail du Centre d'Economie de la Sorbonne 14036, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. Alexander Karpov, 2012. "Equal Weights Coauthorship Sharing and Shapley Value are Equivalen," HSE Working papers WP BRP 03/STI/2012, National Research University Higher School of Economics.

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