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An algorithm for computing the nucleolus of disjunctive non-negative additive games with an acyclic permission structure

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  • van den Brink, René
  • Katsev, Ilya
  • van der Laan, Gerard

Abstract

A cooperative game with a permission structure describes a situation in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. In this paper we consider non-negative additive games with an acyclic permission structure. For such a game we provide a polynomial time algorithm for computing the nucleolus of the induced restricted game. The algorithm is applied to a market situation where sellers can sell objects to buyers through a directed network of intermediaries.

Suggested Citation

  • van den Brink, René & Katsev, Ilya & van der Laan, Gerard, 2010. "An algorithm for computing the nucleolus of disjunctive non-negative additive games with an acyclic permission structure," European Journal of Operational Research, Elsevier, vol. 207(2), pages 817-826, December.
  • Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:817-826
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    References listed on IDEAS

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    1. David McAdams & Michael Schwarz, 2007. "Credible Sales Mechanisms and Intermediaries," American Economic Review, American Economic Association, vol. 97(1), pages 260-276, March.
    2. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer;Game Theory Society, vol. 20(3), pages 277-293.
    3. Hamers, Herbert & Klijn, Flip & Solymosi, Tamas & Tijs, Stef & Vermeulen, Dries, 2003. "On the nucleolus of neighbor games," European Journal of Operational Research, Elsevier, vol. 146(1), pages 1-18, April.
    4. Aldin, Niklas & Stahre, Fredrik, 2003. "Electronic commerce, marketing channels and logistics platforms--a wholesaler perspective," European Journal of Operational Research, Elsevier, vol. 144(2), pages 270-279, January.
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    6. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
    7. Solymosi, Tamas & Raghavan, T. E. S. & Tijs, Stef, 2005. "Computing the nucleolus of cyclic permutation games," European Journal of Operational Research, Elsevier, vol. 162(1), pages 270-280, April.
    8. Muto, Shigeo & Potters, Jos & Tijs, Stef, 1989. "Information Market Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 209-226.
    9. Muto, S. & Potters, J.A.M. & Tijs, S.H., 1989. "Information market games," Other publications TiSEM 2f3f1109-5579-4e6a-9482-e, Tilburg University, School of Economics and Management.
    10. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
    11. René van den Brink & Ilya Katsev & Gerard van der Laan, 2008. "Computation of the Nucleolus for a Class of Disjunctive Games with a Permission Structure," Tinbergen Institute Discussion Papers 08-060/1, Tinbergen Institute.
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    Cited by:

    1. Keyzer, Michiel & van Wesenbeeck, Cornelia, 2011. "Optimal coalition formation and surplus distribution: Two sides of one coin," European Journal of Operational Research, Elsevier, vol. 215(3), pages 604-615, December.
    2. René van den Brink, 2017. "Games with a Permission Structure: a survey on generalizations and applications," Tinbergen Institute Discussion Papers 17-016/II, Tinbergen Institute.
    3. repec:spr:topjnl:v:25:y:2017:i:1:d:10.1007_s11750-017-0440-9 is not listed on IDEAS

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