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The Restricted Core for Totally Positive Games with Ordered Players

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  • Ren� van den Brink

    (VU University Amsterdam)

  • Gerard van der Laan

    (VU University Amsterdam)

  • Valeri Vasil'ev

    (Sobolev Institute of Mathematics, Russia)

Abstract

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many such allocation problems, such as river games, queueing games and auction games, the game is totally positive (i.e., all dividends are nonnegative), and there is some hierarchical ordering of the players. In this paper we introduce the 'Restricted Core' for such 'games with ordered players' which is based on the distribution of 'dividends' taking into account the hierarchical ordering of the players. For totally positive games this solution is always contained in the 'Core', and contains the well-known 'Shapley value' (being the single-valued solution distributing the dividends equally among the players in the corresponding coalitions). For special orderings it equals the Core, respectively Shapley value. We provide an axiomatization and apply this solution to river games.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 09-038/1.

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Date of creation: 00 0000
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Handle: RePEc:dgr:uvatin:20090038

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Related research

Keywords: Totally positive TU-game; Harsanyi dividends; Core; Shapley value; Harsanyi set; Selectope; Digraph; River game;

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References

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  1. René Brink & Gerard Laan & Valeri Vasil’ev, 2007. "Component efficient solutions in line-graph games with applications," Economic Theory, Springer, Springer, vol. 33(2), pages 349-364, November.
  2. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, Springer, vol. 20(3), pages 277-93.
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  9. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, Springer, vol. 26(1), pages 27-43.
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  11. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 12(1), pages 113-126, January.
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  16. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2007. "Distributing Dividends in Games with Ordered Players," Tinbergen Institute Discussion Papers, Tinbergen Institute 06-114/1, Tinbergen Institute.
  17. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print, HAL halshs-00581662, HAL.
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  20. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, Elsevier, vol. 25(2), pages 283-286, October.
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  22. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2004. "On the Extreme Points of Two Polytopes associated with a Digraph and Applications to Cooperative Games," Tinbergen Institute Discussion Papers, Tinbergen Institute 04-069/1, Tinbergen Institute.
  23. Valeri Vasil'ev & Gerard van der Laan, 2001. "The Harsanyi Set for Cooperative TU-Games," Tinbergen Institute Discussion Papers, Tinbergen Institute 01-004/1, Tinbergen Institute.
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