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The Average Tree Permission Value for Games with a Permission Tree

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  • 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. 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.
  2. René Brink & Ilya Katsev & Gerard Laan, 2011. "Axiomatizations of two types of Shapley values for games on union closed systems," Economic Theory, Springer, Springer, vol. 47(1), pages 175-188, May.
  3. René Brink & Gerard Laan & Vitaly Pruzhansky, 2011. "Harsanyi power solutions for graph-restricted games," International Journal of Game Theory, Springer, Springer, vol. 40(1), pages 87-110, February.
  4. Haller, Hans, 1994. "Collusion Properties of Values," International Journal of Game Theory, Springer, Springer, vol. 23(3), pages 261-81.
  5. Brânzei, R. & Fragnelli, V. & Tijs, S.H., 2000. "Tree-connected Peer Group Situations and Peer Group Games," Discussion Paper, Tilburg University, Center for Economic Research 2000-117, Tilburg University, Center for Economic Research.
  6. 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.
  7. 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, American Economic Association, vol. 80(3), pages 493-510, June.
  8. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, INFORMS, vol. 20(3), pages 370-372, November.
  9. 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.
  10. 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.
  11. Ni, Debing & Wang, Yuntong, 2007. "Sharing a polluted river," Games and Economic Behavior, Elsevier, Elsevier, vol. 60(1), pages 176-186, July.
  12. 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.
  13. Baomin Dong & Debing Ni & Yuntong Wang, 2012. "Sharing a Polluted River Network," Environmental & Resource Economics, European Association of Environmental and Resource Economists, European Association of Environmental and Resource Economists, vol. 53(3), pages 367-387, November.
  14. 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.
  15. Gabrielle Demange, 2004. "On group stability in hierarchies and networks," Post-Print, HAL halshs-00581662, HAL.
  16. Faigle, U & Kern, W, 1992. "The Shapley Value for Cooperative Games under Precedence Constraints," International Journal of Game Theory, Springer, Springer, vol. 21(3), pages 249-66.
  17. Béal, Sylvain & Rémila, Eric & Solal, Philippe, 2010. "Rooted-tree solutions for tree games," European Journal of Operational Research, Elsevier, Elsevier, vol. 203(2), pages 404-408, June.
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