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Harsanyi Power Solutions for Graph-restricted 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)
Vitaly Pruzhansky () (Faculty of Economics and Business Administration, Vrije Universiteit Amsterdam)

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Abstract

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A solution for TU-games assigns a set of payoff distributions (possibly empty or consisting of a unique element) to every TU-game. Harsanyi solutions are solutions that are based on distributing dividends. In this paper we consider games with limited communication structure in which the edges or links of an undirected graph on the set of players represent binary communication links between the players such that players can cooperate if and only if they are connected. For such games we discuss Harsanyi solutions whose dividend shares are based on power measures for nodes in corresponding communication graphs. Special attention is given to the Harsanyi degree solution which equals the Shapley value on the class of complete graph games (i.e. the class of TU-games) and equals the position value on the class of cycle-free graph games. Another example is the Harsanyi power solution that is based on the equal power measure, which turns out to be the Myerson value. Various applications of our results are provided.

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Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 04-095/1.

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Date of creation: 27 Aug 2004
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Handle: RePEc:dgr:uvatin:20040095

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Related research
Keywords: cooperative TU-game; Harsanyi dividend; communication structure; power measure; position value; Myerson value; assignment games; auction games;

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

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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. Marco Slikker, 2005. "A characterization of the position value," International Journal of Game Theory, Springer, vol. 33(4), pages 505-514, November. [Downloadable!] (restricted)
  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. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation, Yale University. [Downloadable!]
    Other versions:
  4. 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!]
  5. Branzei, R. & Fragnelli, V. & Tijs, S., 2000. "Tree-connected peer group situations and peer group games," Discussion Paper 117, Tilburg University, Center for Economic Research. [Downloadable!]
  6. Ehud Kalai & Dov Samet, 1983. "On Weighted Shapley Values," Discussion Papers 602, Northwestern University, Center for Mathematical Studies in Economics and Management Science. [Downloadable!]
  7. 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)
  8. 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.
  9. P. Herings & Gerard Laan & Dolf Talman, 2005. "The positional power of nodes in digraphs," Social Choice and Welfare, Springer, vol. 24(3), pages 439-454, 06. [Downloadable!] (restricted)
  10. van den Nouweland, A. & Borm, P. & van Golstein, W. & Bruinderink, R.G. & Tijs, S., 1994. "A Game Theoretic Approach to Problems in Telecommunication," Papers 9407, Tilburg - Center for Economic Research.
  11. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 2003. "Harsanyi Solutions in Line-graph Games," Tinbergen Institute Discussion Papers 03-076/1, Tinbergen Institute. [Downloadable!]
  12. Hamers, H. & Bjorndal, E. & Koster, M, 2003. "Cost allocation in a bank ATM network," Discussion Paper 13, Tilburg University, Center for Economic Research. [Downloadable!]
  13. 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)
  14. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May. [Downloadable!] (restricted)
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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. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J. & Yang, Z.F., 2008. "The Average Tree Solution for Cooperative Games with Communication Structure," Discussion Paper 2008-73, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  2. Herings, P. Jean-Jacques & Laan, Gerard van der & Talman, Dolf, 2005. "The component fairness solution for cycle-free graph games," Discussion Paper 127, Tilburg University, Center for Economic Research. [Downloadable!]
    Other versions:
  3. Baron, Richard & Béal, Sylvain & Remila, Eric & Solal, Philippe, 2008. "Average tree solutions for graph games," MPRA Paper 10189, University Library of Munich, Germany. [Downloadable!]
  4. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2009. "Weighted Component Fairness for Forest Games," MPRA Paper 17455, University Library of Munich, Germany. [Downloadable!]
  5. Amandine Ghintran, 2009. "A weighted position value," Working Papers hal-00420430_v1, HAL. [Downloadable!]
  6. Talman, A.J.J. & Yamamoto, Y., 2007. "Games With Limited Communication Structure," Discussion Paper 2007-19, Tilburg University, Center for Economic Research. [Downloadable!]
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