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Harsanyi Solutions in Line-graph Games

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  • René van den Brink

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Gerard van der Laan

    ()
    (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

  • Valeri Vasil'ev

    ()
    (Sobolev Institute of Mathematics, Novisibirsk)

Abstract

Recently, applications of cooperative game theory to economicallocation problems have gained popularity. To understandthese applications better, economic theory studies thesimilarities and differences between them. The purpose of thispaper is to investigate a special class of cooperative gamesthat generalizes some recent economic applications with asimilar structure. These are so-called line-graph games beingcooperative TU-games in which the players are linearly ordered.Examples of situations that can be modeled like this aresequencing situations, water distribution situations andpolitical majority voting.The main question in cooperative game models of economicsituations is how to allocate the earnings of coalitions amongthe players. We apply the concept of Harsanyi solution toline-graph games. We define four properties that each selectsa unique Harsanyi solution from the class of all Harsanyisolutions. One of these solutions is the well-known Shapleyvalue which is widely applied in economic models. We applythese solutions to the economic situations mentioned above.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 03-076/1.

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Date of creation: 29 Sep 2003
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Handle: RePEc:dgr:uvatin:20030076

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Related research

Keywords: TU-game; Harsanyi dividends; Shapley value; sharing system; Harsanyi solution; line-graph game.;

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References

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  1. (*), Gerard van der Laan & RenÊ van den Brink, 1998. "Axiomatizations of the normalized Banzhaf value and the Shapley value," Social Choice and Welfare, Springer, Springer, vol. 15(4), pages 567-582.
  2. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, Elsevier, vol. 100(2), pages 274-294, October.
  3. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, Elsevier, vol. 109(1), pages 90-103, March.
  4. Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A, University of Bonn, Germany 338, University of Bonn, Germany.
  5. Potters, Jos & Reijnierse, Hans, 1995. "Gamma-Component Additive Games," International Journal of Game Theory, Springer, Springer, vol. 24(1), pages 49-56.
  6. René van den Brink, 2002. "An axiomatization of the Shapley value using a fairness property," International Journal of Game Theory, Springer, Springer, vol. 30(3), pages 309-319.
  7. Valeri Vasil'ev & Gerard van der Laan, 2001. "The Harsanyi Set for Cooperative TU-Games," Tinbergen Institute Discussion Papers, Tinbergen Institute 01-004/1, Tinbergen Institute.
  8. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, Springer, vol. 29(1), pages 23-38.
  9. Borm, P.E.M. & Nouweland, C.G.A.M. van den & Tijs, S.H., 1991. "Cooperation and communication restrictions: A survey," Research Memorandum, Tilburg University, Faculty of Economics and Business Administration 507, Tilburg University, Faculty of Economics and Business Administration.
  10. Gilles, Robert P & Owen, Guillermo & van den Brink, Rene, 1992. "Games with Permission Structures: The Conjunctive Approach," International Journal of Game Theory, Springer, Springer, vol. 20(3), pages 277-93.
  11. Jesßs-Mario Bilbao, 1998. "Values and potential of games with cooperation structure," International Journal of Game Theory, Springer, Springer, vol. 27(1), pages 131-145.
  12. Borm, P.E.M. & Fernández, C. & Hendrickx, R.L.P. & Tijs, S.H., 2005. "Drop out monotonic rules for sequencing situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-171917, Tilburg University.
  13. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, Elsevier, vol. 12(1), pages 113-126, January.
  14. RenÊ van den Brink, 1997. "An Axiomatization of the Disjunctive Permission Value for Games with a Permission Structure," International Journal of Game Theory, Springer, Springer, vol. 26(1), pages 27-43.
  15. Algaba, A. & Bilbao, J.M. & Brink, J.R. van den & Jiménez-Losada, A., 2000. "Cooperative Games on Antimatroids," Discussion Paper, Tilburg University, Center for Economic Research 2000-124, Tilburg University, Center for Economic Research.
  16. Jean Derks & Gerard van der Laan & Valeri Vasil'ev, 2002. "On Harsanyi Payoff Vectors and the Weber Set," Tinbergen Institute Discussion Papers, Tinbergen Institute 02-105/1, Tinbergen Institute.
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Citations

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Cited by:
  1. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers, Tinbergen Institute 04-095/1, Tinbergen Institute.
  2. Lei Li & Xueliang Li, 2011. "The covering values for acyclic digraph games," International Journal of Game Theory, Springer, Springer, vol. 40(4), pages 697-718, November.
  3. René van den Brink, 2003. "Axiomatizations of Permission Values for Games with a Hierarchical Permission Structure using Split Neutrality," Tinbergen Institute Discussion Papers, Tinbergen Institute 03-100/1, Tinbergen Institute.

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