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

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

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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Article provided by Elsevier in its journal European Journal of Operational Research.

Volume (Year): 207 (2010)
Issue (Month): 2 (December)
Pages: 817-826

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Handle: RePEc:eee:ejores:v:207:y:2010:i:2:p:817-826
Contact details of provider: Web page: http://www.elsevier.com/locate/eor

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  1. Muto, Shigeo & Potters, Jos & Tijs, Stef, 1989. "Information Market Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 18(2), pages 209-26.
  2. Rodica Brânzei & Tamás Solymosi & Stef Tijs, 2005. "Strongly essential coalitions and the nucleolus of peer group games," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(3), pages 447-460, 09.
  3. Gilles, R.P. & Owen, G. & van den Brink, J.R., 1991. "Games with permission structures : The conjunctive approach," Discussion Paper 1991-14, Tilburg University, Center for Economic Research.
  4. 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.
  5. van den Brink, J.R. & Gilles, R.P., 1991. "Axiomatizations of the conjunctive permission value for games with permission structures," Research Memorandum FEW 485, Tilburg University, School of Economics and Management.
  6. 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.
  7. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
  8. 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.
  9. David McAdams & Michael Schwarz, 2007. "Credible Sales Mechanisms and Intermediaries," American Economic Review, American Economic Association, vol. 97(1), pages 260-276, March.
  10. 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.
  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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