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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)

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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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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.;

Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

This paper has been announced in the following NEP Reports:

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Fernandez, C. & Borm, P. & Hendrickx, R. & Tijs, S., 2002. "Drop out monotonic rules for sequencing situations," Discussion Paper 51, Tilburg University, Center for Economic Research. [Downloadable!]
  2. 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.
  3. (*), 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. [Downloadable!] (restricted)
  4. Perez-Castrillo, David & Wettstein, David, 2001. "Bidding for the Surplus : A Non-cooperative Approach to the Shapley Value," Journal of Economic Theory, Elsevier, vol. 100(2), pages 274-294, October. [Downloadable!] (restricted)
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  5. Maniquet, Francois, 2003. "A characterization of the Shapley value in queueing problems," Journal of Economic Theory, Elsevier, vol. 109(1), pages 90-103, March. [Downloadable!] (restricted)
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  6. Brink, R. van den, 1999. "An axiomatization of the shapley value using a fairness property," Discussion Paper 120, Tilburg University, Center for Economic Research. [Downloadable!]
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  7. Valeri Vasil'ev & Gerard van der Laan, 2001. "The Harsanyi Set for Cooperative TU-Games," Tinbergen Institute Discussion Papers 01-004/1, Tinbergen Institute. [Downloadable!]
  8. Le Breton, M & Owen, G & Weber, S, 1992. "Strongly Balanced Cooperative Games," International Journal of Game Theory, Springer, vol. 20(4), pages 419-27.
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  9. 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. [Downloadable!] (restricted)
  10. 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.
  11. 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. [Downloadable!]
  12. Potters, Jos & Reijnierse, Hans, 1995. "Gamma-Component Additive Games," International Journal of Game Theory, Springer, vol. 24(1), pages 49-56.
  13. Jesßs-Mario Bilbao, 1998. "Values and potential of games with cooperation structure," International Journal of Game Theory, Springer, vol. 27(1), pages 131-145. [Downloadable!] (restricted)
  14. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer, vol. 29(1), pages 23-38. [Downloadable!] (restricted)
  15. Algaba, E. & Bilbao, J.M. & Brink, R. van den, 2000. "Cooperative games on antimatroids," Discussion Paper 124, Tilburg University, Center for Economic Research. [Downloadable!]
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(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. 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. [Downloadable!]
  2. René van den Brink & Gerard van der Laan & Vitaly Pruzhansky, 2004. "Harsanyi Power Solutions for Graph-restricted Games," Tinbergen Institute Discussion Papers 04-095/1, Tinbergen Institute. [Downloadable!]
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