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The core of games on ordered structures and graphs

  • Michel Grabisch

    ()

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

In cooperative games, the core is the most popular solution concept, and its properties are well known. In the classical setting of cooperative games, it is generally assumed that all coalitions can form, i.e., they are all feasible. In many situations, this assumption is too strong and one has to deal with some unfeasible coalitions. Defining a game on a subcollection of the power set of the set of players has many implications on the mathematical structure of the core, depending on the precise structure of the subcollection of feasible coalitions. Many authors have contributed to this topic, and we give a unified view of these different results.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00445171.

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Date of creation: Oct 2009
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Publication status: Published in 4OR: A Quarterly Journal of Operations Research, Springer Verlag, 2009, 7 (3), pp.207-238. <10.1007/s10288-009-0109-9>
Handle: RePEc:hal:cesptp:halshs-00445171
DOI: 10.1007/s10288-009-0109-9
Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-00445171
Contact details of provider: Web page: https://hal.archives-ouvertes.fr/

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  3. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00563926, HAL.
  4. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
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  6. van den Nouweland, C.G.A.M. & Borm, P.E.M. & Tijs, S.H., 1992. "Allocation rules for hypergraph communication situations," Other publications TiSEM b97fb9dd-2acf-470d-b9eb-a, Tilburg University, School of Economics and Management.
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  8. 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.
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  14. 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.
  15. Michel Grabisch, 2009. "The core of games on ordered structures and graphs," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445171, HAL.
  16. Itzhak Gilboa & Ehud Lehrer, 1990. "Global Games," Discussion Papers 922, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
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  19. Ulrich Faigle & Michel Grabisch & Maximilian Heyne, 2010. "Monge extensions of cooperation and communication structures," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00625336, HAL.
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  24. 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.
  25. 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.
  26. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," Annals of Operations Research, Springer, vol. 204(1), pages 33-64, April.
  27. Derks, Jean J M & Gilles, Robert P, 1995. "Hierarchical Organization Structures and Constraints on Coalition Formation," International Journal of Game Theory, Springer;Game Theory Society, vol. 24(2), pages 147-63.
  28. Michel Grabisch, 2013. "The core of games on ordered structures and graphs," PSE - Labex "OSE-Ouvrir la Science Economique" hal-00803233, HAL.
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