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The Average Tree Permission Value for Games with a Permission Tree

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Author Info

  • Rene van den Brink

    (VU University Amsterdam)

  • Jean-Jacques Herings

    (Maastricht University)

  • Gerard van der Laan

    (VU University Amsterdam)

  • Dolf Talman

    (Tilburg University)

Abstract

In the literature various models of games with restricted cooperation can be found. In those models, instead of allowing for all subsets of the set of players to form, it is assumed that the set of feasible coalitions is a proper subset of the power set of the set of players. In this paper we consider such sets of feasible coalitions that follow from a permission structure on the set of players, in which players need permission to cooperate with other players. We assume the permission structure to be an oriented tree. This means that there is one player at the top of the permission structure and for every other player there is a unique directed path from the top player to this player. We introduce a new solution for these games based on the idea of the Average Tree value for cycle-free communication graph games. We provide two axiomatizations for this new value and compare it with the conjunctive permission value.

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Bibliographic Info

Paper provided by Tinbergen Institute in its series Tinbergen Institute Discussion Papers with number 13-023/II.

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Date of creation: 24 Jan 2012
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Handle: RePEc:dgr:uvatin:20130023

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Web page: http://www.tinbergen.nl

Related research

Keywords: TU game; restricted cooperation; permission structure; Shapley value; Average Tree value; axiomatization;

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References

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  1. Herings, P.J.J. & Laan, G. van der & Talman, A.J.J., 2008. "The average tree solution for cycle-free graph games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-377604, Tilburg University.
  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.
  3. Rene van den Brink & Ilya Katsev & Gerard van der Laan, 2009. "Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems," Tinbergen Institute Discussion Papers 09-064/1, Tinbergen Institute.
  4. Graham, Daniel A & Marshall, Robert C & Richard, Jean-Francois, 1990. "Differential Payments within a Bidder Coalition and the Shapley Value," American Economic Review, American Economic Association, vol. 80(3), pages 493-510, June.
  5. Gabrielle Demange, 2004. "On Group Stability in Hierarchies and Networks," Journal of Political Economy, University of Chicago Press, vol. 112(4), pages 754-778, August.
  6. Dong, Baomin & Ni, Debing & Wang, Yuntong, 2012. "Sharing a polluted river network," MPRA Paper 38839, University Library of Munich, Germany.
  7. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, vol. 60(1), pages 176-186, July.
  8. 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.
  9. 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.
  10. Brânzei, R. & Fragnelli, V. & Tijs, S.H., 2002. "Tree-connected peer group situations and peer group games," Open Access publications from Tilburg University urn:nbn:nl:ui:12-91321, Tilburg University.
  11. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
  12. 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.
  13. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, vol. 21(3), pages 249-66.
  14. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, vol. 23(3), pages 261-81.
  15. Borm, P.E.M. & Owen, G. & Tijs, S.H., 1992. "On the position value for communication situations," Open Access publications from Tilburg University urn:nbn:nl:ui:12-154855, Tilburg University.
  16. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, vol. 203(2), pages 404-408, June.
  17. Béal, Sylvain & Lardon, Aymeric & Rémila, Eric & Solal, Philippe, 2011. "The Average Tree Solution for Multi-choice Forest Games," MPRA Paper 28739, University Library of Munich, Germany.
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