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

Author

Listed:
  • Derks, J.

    (Externe publicaties SBE)

  • Peters, H.J.M.

    (Quantitative Economics)

  • Sudhölter, P.

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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Suggested Citation

  • Derks, J. & Peters, H.J.M. & Sudhölter, P., 2012. "On extensions of the core and the anticore of transferable utility games," Research Memorandum 003, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
    • Handle: RePEc:unm:umamet:2012003
    DOI: 10.26481/umamet.2012003
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    Cited by:

    1. Karpov, Alexander, 2014. "Equal weights coauthorship sharing and the Shapley value are equivalent," Journal of Informetrics, Elsevier, vol. 8(1), pages 71-76.
    2. Fatma Aslan & Papatya Duman & Walter Trockel, 2019. "Duality for General TU-games Redefined," Working Papers CIE 121, Paderborn University, CIE Center for International Economics.
    3. Michel Grabisch & Peter Sudhölter, 2016. "Characterizations of solutions for games with precedence constraints," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01297600, HAL.
    4. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Efficiency and Duality," Working Papers CIE 138, Paderborn University, CIE Center for International Economics.
    5. Fatma Aslan & Papatya Duman & Walter Trockel, 2020. "Non-cohesive TU-games: Duality and P-core," Working Papers CIE 136, Paderborn University, CIE Center for International Economics.
    6. 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.
    7. Chen, Haoxun, 2017. "Undominated nonnegative excesses and core extensions of transferable utility games," European Journal of Operational Research, Elsevier, vol. 261(1), pages 222-233.
    8. Michel Grabisch & Hervé Moulin & José Manuel Zarzuelo, 2024. "Professor Peter Sudhölter (1957–2024)," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 289-294, June.
    9. Moshe Babaioff & Uriel Feige, 2019. "A New Approach to Fair Distribution of Welfare," Papers 1909.11346, arXiv.org.

    More about this item

    JEL classification:

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

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