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Computing the Nucleolus When the Characteristic Function Is Given Implicitly: A Constraint Generation Approach

Author

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  • Hallefjord, Asa
  • Helming, Reidun
  • Jornsten, Kurt

Abstract

We study a class of cooperative games that is such that the values of the characteristic function are given implicitly. A constraint generation procedure can be applied to compute the nucleolus (and related solutions) of such a game, even if the number of players is large.

Suggested Citation

  • Hallefjord, Asa & Helming, Reidun & Jornsten, Kurt, 1995. "Computing the Nucleolus When the Characteristic Function Is Given Implicitly: A Constraint Generation Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(4), pages 357-372.
    • Handle: RePEc:spr:jogath:v:24:y:1995:i:4:p:357-72
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    Cited by:

    1. Ralf Borndörfer & Nam-Dũng Hoang, 2015. "Fair ticket pricing in public transport as a constrained cost allocation game," Annals of Operations Research, Springer, vol. 226(1), pages 51-68, March.
    2. Karaca, Orcun & Delikaraoglou, Stefanos & Hug, Gabriela & Kamgarpour, Maryam, 2022. "Enabling inter-area reserve exchange through stable benefit allocation mechanisms," Omega, Elsevier, vol. 113(C).
    3. Stefan Engevall & Maud Göthe-Lundgren & Peter Värbrand, 2004. "The Heterogeneous Vehicle-Routing Game," Transportation Science, INFORMS, vol. 38(1), pages 71-85, February.
    4. Kimms, Alf & Çetiner, Demet, 2012. "Approximate nucleolus-based revenue sharing in airline alliances," European Journal of Operational Research, Elsevier, vol. 220(2), pages 510-521.
    5. Guajardo, Mario & Jörnsten, Kurt, 2015. "Common mistakes in computing the nucleolus," European Journal of Operational Research, Elsevier, vol. 241(3), pages 931-935.
    6. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
    7. Lu, Wei & Quadrifoglio, Luca, 2019. "Fair cost allocation for ridesharing services – modeling, mathematical programming and an algorithm to find the nucleolus," Transportation Research Part B: Methodological, Elsevier, vol. 121(C), pages 41-55.
    8. Lozano, S., 2012. "Information sharing in DEA: A cooperative game theory approach," European Journal of Operational Research, Elsevier, vol. 222(3), pages 558-565.

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