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Computing an Element in the Lexicographic Kernel of a Game

Author

Listed:
  • Ulrich Faigle
  • Walter Kern
  • Jeroen Kuipers

Abstract

The lexicographic kernel of a game lexicographically maximizes the surplusses s ij (rather than the excesses as would the nucleolus) and is contained in both the least core and the kernel. We show that an element in the lexicographic kernel can be computed efficiently, provided we can efficiently compute the surplusses s ij (x) corresponding to a given allocation x. This approach improves the results in Faigle et al. (in Int J Game Theory 30:79–98, 2001) and allows us to determine a kernel element without appealing to Maschler transfers in the execution of the algorithm. Copyright Springer-Verlag 2006

Suggested Citation

  • Ulrich Faigle & Walter Kern & Jeroen Kuipers, 2006. "Computing an Element in the Lexicographic Kernel of a Game," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(3), pages 427-433, July.
    • Handle: RePEc:spr:mathme:v:63:y:2006:i:3:p:427-433
    DOI: 10.1007/s00186-006-0065-5
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    References listed on IDEAS

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    1. Jeroen Kuipers & Ulrich Faigle & Walter Kern, 2001. "On the computation of the nucleolus of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 79-98.
    2. Moshe Yarom, 1981. "The Lexicographic Kernel of a Cooperative Game," Mathematics of Operations Research, INFORMS, vol. 6(1), pages 88-100, February.
    3. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    4. Ulrich Faigle & Walter Kern & Winfried Hochstättler & Sándor P. Fekete, 1997. "On the Complexity of Testing Membership in the Core of Min-Cost Spanning Tree Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(3), pages 361-366.
    5. Walter Kern & Daniël Paulusma, 2003. "Matching Games: The Least Core and the Nucleolus," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 294-308, May.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Kernel; Lexicographic; Computational complexity; 90C27; 90D12;
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