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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.

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  • 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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    Cited by:

    1. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2023. "Properties of Solutions for Games on Union-Closed Systems," Mathematics, MDPI, vol. 11(4), pages 1-16, February.
    2. 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.
    3. 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.
    4. Natalia I. Naumova, 2022. "Some solutions for generalized games with restricted cooperation," Annals of Operations Research, Springer, vol. 318(2), pages 1077-1093, November.
    5. René Brink, 2017. "Games with a permission structure - A survey on generalizations and applications," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 1-33, April.

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