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Share functions for cooperative games with levels structure of cooperation

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  • Álvarez-Mozos, M.
  • van den Brink, R.
  • van der Laan, G.
  • Tejada, O.

Abstract

In a standard TU-game it is assumed that every subset of the player set N can form a coalition and earn its worth. One of the first models where restrictions in cooperation are considered is the one of games with coalition structure of Aumann and Drèze (1974). They assumed that the player set is partitioned into unions and that players can only cooperate within their own union. Owen (1977) introduced a value for games with coalition structure under the assumption that also the unions can cooperate among them. Winter (1989) extended this value to games with levels structure of cooperation, which consists of a game and a finite sequence of partitions defined on the player set, each of them being coarser than the previous one.

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Bibliographic Info

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

Volume (Year): 224 (2013)
Issue (Month): 1 ()
Pages: 167-179

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Handle: RePEc:eee:ejores:v:224:y:2013:i:1:p:167-179

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

Related research

Keywords: Cooperative game; Shapley value; Coalition structure; Share functions; Levels structure of cooperation;

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  1. Brink, J.R. van den & Laan, G. van der, 2001. "A Class of Consistent Share Functions For Games in Coalition Structure," Discussion Paper 2001-33, Tilburg University, Center for Economic Research.
  2. Albizuri, M.J. & Aurrecoechea, J. & Zarzuelo, J.M., 2006. "Configuration values: Extensions of the coalitional Owen value," Games and Economic Behavior, Elsevier, vol. 57(1), pages 1-17, October.
  3. M. Albizuri & Jesus Aurrekoetxea, 2006. "Coalition Configurations and the Banzhaf Index," Social Choice and Welfare, Springer, vol. 26(3), pages 571-596, June.
  4. Winter, Eyal, 1989. "A Value for Cooperative Games with Levels Structure of Cooperation," International Journal of Game Theory, Springer, vol. 18(2), pages 227-40.
  5. Sébastien Courtin, 2011. "Power in the European Union: an evaluation according to a priori relations between states," Economics Bulletin, AccessEcon, vol. 31(1), pages 534-545.
  6. Gerard van der Laan & René van den Brink, 1998. "Axiomatization of a class of share functions for n-person games," Theory and Decision, Springer, vol. 44(2), pages 117-148, April.
  7. Brink, J.R. van den & Laan, G. van der, 1998. "The normalized Banzhaf value and the Banzhaf share function," Research Memorandum 764, Tilburg University, Faculty of Economics and Business Administration.
  8. Gerard van der Laan & René van den Brink, 2002. "A Banzhaf share function for cooperative games in coalition structure," Theory and Decision, Springer, vol. 53(1), pages 61-86, August.
  9. Pekec, Aleksandar, 2001. "Meaningful and meaningless solutions for cooperative n-person games," European Journal of Operational Research, Elsevier, vol. 133(3), pages 608-623, September.
  10. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, vol. 15(4), pages 567-582.
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