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Harsanyi Solutions in Line-graph Games

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Author Info

  • 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 economic allocation problems have gained popularity. To understand these applications better, economic theory studies the similarities and differences between them. The purpose of this paper is to investigate a special class of cooperative games that generalizes some recent economic applications with a similar structure. These are so-called line-graph games being cooperative TU-games in which the players are linearly ordered. Examples of situations that can be modeled like this are sequencing situations, water distribution situations and political majority voting. The main question in cooperative game models of economic situations is how to allocate the earnings of coalitions among the players. We apply the concept of Harsanyi solution to line-graph games. We define four properties that each selects a unique Harsanyi solution from the class of all Harsanyi solutions. One of these solutions is the well-known Shapley value which is widely applied in economic models. We apply these 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. 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. Brink, J.R. van den, 1999. "An Axiomatization of the Shapley Value Using a Fairness Property," Discussion Paper 1999-120, Tilburg University, Center for Economic Research.
  3. Maniquet, F., 2000. "A Characterization of the Shapley Value in Queueing Problems," Papers 222, Notre-Dame de la Paix, Sciences Economiques et Sociales.
  4. Le Breton,Michel & Owen,Guillermo & Weber,Shlomo, 1991. "Strongly balanced cooperative games," Discussion Paper Serie A 338, University of Bonn, Germany.
  5. Jean Derks & Gerard van der Laan & Valeri Vasil'ev, 2002. "On Harsanyi Payoff Vectors and the Weber Set," Tinbergen Institute Discussion Papers 02-105/1, Tinbergen Institute.
  6. Gilles, R.P. & Owen, G. & Brink, J.R. van den, 1991. "Games with permission structures: The conjunctive approach," Discussion Paper 1991-14, Tilburg University, Center for Economic Research.
  7. Borm, P.E.M. & Nouweland, C.G.A.M. van den & Tijs, S.H., 1994. "Cooperation and communication restrictions: A survey," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154189, Tilburg University.
  8. Valeri Vasil'ev & Gerard van der Laan, 2001. "The Harsanyi Set for Cooperative TU-Games," Tinbergen Institute Discussion Papers 01-004/1, Tinbergen Institute.
  9. Derks, Jean & Haller, Hans & Peters, Hans, 2000. "The selectope for cooperative games," Open Access publications from Maastricht University urn:nbn:nl:ui:27-12221, Maastricht University.
  10. Potters, Jos & Reijnierse, Hans, 1995. "Gamma-Component Additive Games," International Journal of Game Theory, Springer, vol. 24(1), pages 49-56.
  11. Fernández, C. & Borm, P.E.M. & Hendrickx, R.L.P. & Tijs, S.H., 2002. "Drop Out Monotonic Rules for Sequencing Situations," Discussion Paper 2002-51, Tilburg University, Center for Economic Research.
  12. van den Brink, Rene & Gilles, Robert P., 1996. "Axiomatizations of the Conjunctive Permission Value for Games with Permission Structures," Games and Economic Behavior, Elsevier, vol. 12(1), pages 113-126, January.
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  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, vol. 26(1), pages 27-43.
  15. (*), 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.
  16. Jesßs-Mario Bilbao, 1998. "Values and potential of games with cooperation structure," International Journal of Game Theory, Springer, vol. 27(1), pages 131-145.
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Citations

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Cited by:
  1. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer, vol. 40(1), pages 87-110, February.
  2. René van den Brink, 2003. "Axiomatizations of Permission Values for Games with a Hierarchical Permission Structure using Split Neutrality," Tinbergen Institute Discussion Papers 03-100/1, Tinbergen Institute.
  3. Lei Li & Xueliang Li, 2011. "The covering values for acyclic digraph games," International Journal of Game Theory, Springer, vol. 40(4), pages 697-718, November.

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