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Monge extensions of cooperation and communication structures

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  • Faigle, U.
  • Grabisch, M.
  • Heyne, M.

Abstract

Cooperation structures without any a priori assumptions on the combinatorial structure of feasible coalitions are studied and a general theory for marginal values, cores and convexity is established. The theory is based on the notion of a Monge extension of a general characteristic function, which is equivalent to the Lovász extension in the special situation of a classical cooperative game. It is shown that convexity of a cooperation structure is tantamount to the equality of the associated core and Weber set. Extending Myerson's graph model for game theoretic communication, general communication structures are introduced and it is shown that a notion of supermodularity exists for this class that characterizes convexity and properly extends Shapley's convexity model for classical cooperative games.

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Bibliographic Info

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

Volume (Year): 206 (2010)
Issue (Month): 1 (October)
Pages: 104-110

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Handle: RePEc:eee:ejores:v:206:y:2010:i:1:p:104-110

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Web page: http://www.elsevier.com/locate/eor

Related research

Keywords: 91A12 91A40 Communication structure Convex game Cooperation structure Monge extension Lovasz extension Marginal value Ranking Shapley value Supermodularity Weber set;

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References

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  1. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
  2. 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.
  3. Borm, P.E.M. & Algaba, A. & Bilbao, J.M. & Lopez, J., 2002. "The Myerson value for union stable systems," Open Access publications from Tilburg University urn:nbn:nl:ui:12-90189, Tilburg University.
  4. 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.
  5. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, vol. 20(3), pages 277-93.
  6. repec:hal:cesptp:halshs-00178916 is not listed on IDEAS
  7. 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.
  8. 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.
  9. E. Algaba & J.M. Bilbao & J.R. Fernández & A. Jiménez, 2004. "The Lovász Extension of Market Games," Theory and Decision, Springer, vol. 56(2_2), pages 229-238, 02.
  10. 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.
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Citations

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Cited by:
  1. repec:hal:cesptp:halshs-00544134 is not listed on IDEAS
  2. repec:hal:cesptp:halshs-00445171 is not listed on IDEAS
  3. Koshevoy, G.A. & Talman, A.J.J., 2011. "Solution Concepts for Games with General Coalitional Structure (Replaces CentER DP 2011-025)," Discussion Paper 2011-119, Tilburg University, Center for Economic Research.
  4. Koshevoy, G.A. & Suzuki, T. & Talman, A.J.J., 2013. "Solutions For Games With General Coalitional Structure And Choice Sets," Discussion Paper 2013-012, Tilburg University, Center for Economic Research.
  5. Michel Grabisch & Peter Sudhölter, 2012. "On the restricted cores and the bounded core of games on distributive lattices," Documents de travail du Centre d'Economie de la Sorbonne 12067, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
  6. Encarnacion Algaba & Jesus Mario Bilbao & Rene van den Brink, 2011. "Harsanyi Power Solutions for Games on Union Stable Systems," Tinbergen Institute Discussion Papers 11-182/1, Tinbergen Institute.
  7. repec:hal:cesptp:hal-00650964 is not listed on IDEAS
  8. repec:hal:cesptp:hal-00803233 is not listed on IDEAS
  9. Encarnacion Algaba & Jesus Mario Bilbao & Rene van den Brink & Jorge J. Lopez, 2011. "The Myerson Value and Superfluous Supports in Union Stable Systems," Tinbergen Institute Discussion Papers 11-127/1, Tinbergen Institute.
  10. Koshevoy, Gleb & Talman, Dolf, 2014. "Solution concepts for games with general coalitional structure," Mathematical Social Sciences, Elsevier, vol. 68(C), pages 19-30.
  11. Encarnacion Algaba & Jesus Mario Bilbao & Rene van den Brink & Jorge J. Lopez, 2011. "The Myerson Value and Superfluous Supports in Union Stable Systems," Tinbergen Institute Discussion Papers 11-127/1, Tinbergen Institute.
  12. 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.
  13. Encarnacion Algaba & Jesus Mario Bilbao & Rene van den Brink, 2011. "Harsanyi Power Solutions for Games on Union Stable Systems," Tinbergen Institute Discussion Papers 11-182/1, Tinbergen Institute.

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