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On the restricted cores and the bounded core of games on distributive lattices

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  • Michel Grabisch

    ()
    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne, EEP-PSE - Ecole d'Économie de Paris - Paris School of Economics - Ecole d'Économie de Paris)

  • Peter Sudhölter

    ()
    (University of Southern Denmark - Department of Business and Economics and COHERE)

Abstract

We consider TU-games with restricted cooperation, where the set of feasible coalitions is a distributive lattice, hence generated by a partial order on the set of players. In such a situation, the core may be unbounded, and one has to select a bounded part of the core as a solution concept. The restricted core is obtained by imposing equality constraints in the core for sets belonging to so-called normal collections, resulting (if nonempty) in the selection of a bounded face of the core. The bounded core proves to be the union of all bounded faces (restricted cores). The paper aims at investigating in depth the relation between the bounded core and restricted cores, as well as the properties and structures of the restricted cores and normal collections. In particular, it is found that a game is convex if and only if all restricted cores corresponding to the minimal nested normal collections are nonempty. Moreover, in this case the union of these restricted cores already covers the bounded core.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00748331.

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Date of creation: Oct 2012
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Handle: RePEc:hal:cesptp:halshs-00748331

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Keywords: TU-game; restricted cooperation; distributive lattice; core; extremal rays; faces of the core.;

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  1. Michel Grabisch & Peter Sudhölter, 2012. "The bounded core for games with precedence constraints," Documents de travail du Centre d'Economie de la Sorbonne 12006, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  2. repec:hal:cesptp:hal-00759893 is not listed on IDEAS
  3. Bilbao, J. M., 1998. "Axioms for the Shapley value on convex geometries," European Journal of Operational Research, Elsevier, vol. 110(2), pages 368-376, October.
  4. repec:hal:journl:halshs-00673909 is not listed on IDEAS
  5. Bilbao, J. M. & Lebron, E. & Jimenez, N., 1999. "The core of games on convex geometries," European Journal of Operational Research, Elsevier, vol. 119(2), pages 365-372, December.
  6. Péter Csóka & P. Jean-Jacques Herings & László Á. Kóczy, 2007. "Balancedness Conditions for Exact Games," Working Paper Series 0805, Óbuda University, Keleti Faculty of Business and Management, revised May 2008.
  7. Michel Grabisch & Lijue Xie, 2008. "The core of games on distributive lattices : how to share benefits in a hierarchy," Documents de travail du Centre d'Economie de la Sorbonne b08077, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne, revised Sep 2009.
  8. Pulido, Manuel A. & Sanchez-Soriano, Joaquin, 2006. "Characterization of the core in games with restricted cooperation," European Journal of Operational Research, Elsevier, vol. 175(2), pages 860-869, December.
  9. Michel Grabisch, 2010. "Ensuring the boundedness of the core of games with restricted cooperation," Documents de travail du Centre d'Economie de la Sorbonne 10093, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  10. Michel Grabisch & Lijue Xie, 2011. "The restricted core of games on distributive lattices: how to share benefits in a hierarchy," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00583868, HAL.
  11. repec:hal:journl:halshs-00344802 is not listed on IDEAS
  12. repec:hal:journl:halshs-00583868 is not listed on IDEAS
  13. repec:hal:journl:halshs-00445171 is not listed on IDEAS
  14. Michel Grabisch, 2009. "The core of games on ordered structures and graphs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445171, HAL.
  15. Peter Sudhölter & Yan-An Hwang, 2001. "Axiomatizations of the core on the universal domain and other natural domains," International Journal of Game Theory, Springer, vol. 29(4), pages 597-623.
  16. repec:hal:cesptp:hal-00625336 is not listed on IDEAS
  17. Ichiishi, Tatsuro, 1981. "Super-modularity: Applications to convex games and to the greedy algorithm for LP," Journal of Economic Theory, Elsevier, vol. 25(2), pages 283-286, October.
  18. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, vol. 21(3), pages 249-66.
  19. Derks, Jean J M & Gilles, Robert P, 1995. "Hierarchical Organization Structures and Constraints on Coalition Formation," International Journal of Game Theory, Springer, vol. 24(2), pages 147-63.
  20. Algaba, A. & Bilbao, J.M. & Brink, J.R. van den & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Discussion Paper 2000-124, Tilburg University, Center for Economic Research.
  21. Faigle, U. & Grabisch, M. & Heyne, M., 2010. "Monge extensions of cooperation and communication structures," European Journal of Operational Research, Elsevier, vol. 206(1), pages 104-110, October.
  22. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
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