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Implementation of weighted values in hierarchical and horizontal cooperation structures

  • Kamijo, Yoshio

This paper studies a non-cooperative mechanism implementing a cooperative solution for a situation in which members of a society are subdivided into groups and/or coalitions and there is asymmetry among the individuals of the society. To describe hierarchical and horizontal cooperation structure simultaneously, we present unified classes of games, the games with social structure, and define a weighted value for these games. We show that our mechanism works in any zero-monotonic environment and implements the Shapley value, the weighted Shapley value, the Owen's coalitional value, and the weighted coalitional value, in some special cases.

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Article provided by Elsevier in its journal Mathematical Social Sciences.

Volume (Year): 56 (2008)
Issue (Month): 3 (November)
Pages: 336-349

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Handle: RePEc:eee:matsoc:v:56:y:2008:i:3:p:336-349
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/505565

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  1. David Pérez-Castrillo & David Wettstein, . "Bidding For The Surplus: A Non-Cooperative Approach To The Shapley Value," UFAE and IAE Working Papers 461.00, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Sergiu Hart & Andreu Mas-Colell, 1994. "Bargaining and value," Economics Working Papers 114, Department of Economics and Business, Universitat Pompeu Fabra, revised Feb 1995.
  3. David P�rez-Castrillo & David Wettstein, 2002. "Choosing Wisely: A Multibidding Approach," American Economic Review, American Economic Association, vol. 92(5), pages 1577-1587, December.
  4. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
  5. Vidal-Puga, Juan & Bergantinos, Gustavo, 2003. "An implementation of the Owen value," Games and Economic Behavior, Elsevier, vol. 44(2), pages 412-427, August.
  6. Levy, Anat & Mclean, Richard P., 1989. "Weighted coalition structure values," Games and Economic Behavior, Elsevier, vol. 1(3), pages 234-249, September.
  7. Bloch, Francis & Dutta, Bhaskar, 2005. "Communication Networks with Endogenous Link Strength," The Warwick Economics Research Paper Series (TWERPS) 723, University of Warwick, Department of Economics.
  8. David Pérez-Castrillo & David Wettstein, 2004. "Forming Efficient Networks," UFAE and IAE Working Papers 609.04, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  9. Juan Vidal-Puga, 2005. "A bargaining approach to the Owen value and the Nash solution with coalition structure," Economic Theory, Springer, vol. 25(3), pages 679-701, 04.
  10. Slikker, Marco, 2007. "Bidding for surplus in network allocation problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 493-511, November.
  11. Maschler, M & Owen, G, 1989. "The Consistent Shapley Value for Hyperplane Games," International Journal of Game Theory, Springer, vol. 18(4), pages 389-407.
  12. Mutuswami, Suresh & Perez-Castrillo, David & Wettstein, David, 2004. "Bidding for the surplus: realizing efficient outcomes in economic environments," Games and Economic Behavior, Elsevier, vol. 48(1), pages 111-123, July.
  13. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Other publications TiSEM 5a8473e4-1df7-42df-ad53-f, Tilburg University, School of Economics and Management.
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