The Average Tree Permission Value for Games with a Permission Tree

R. van den Brink, P.J.J. Herings, G. van der Laan, A.J.J. Talman

Research output: Working paperDiscussion paperOther research output

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Abstract

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.
Original languageEnglish
Place of PublicationTilburg
PublisherEconometrics
Number of pages25
Volume2013-001
Publication statusPublished - 2013

Publication series

NameCentER Discussion Paper
Volume2013-001

Fingerprint

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Keywords

  • TU game
  • restricted cooperation
  • permission structure
  • Shapley value
  • Average Tree value
  • axiomatization

Cite this

van den Brink, R., Herings, P. J. J., van der Laan, G., & Talman, A. J. J. (2013). The Average Tree Permission Value for Games with a Permission Tree. (CentER Discussion Paper; Vol. 2013-001). Tilburg: Econometrics.
van den Brink, R. ; Herings, P.J.J. ; van der Laan, G. ; Talman, A.J.J. / The Average Tree Permission Value for Games with a Permission Tree. Tilburg : Econometrics, 2013. (CentER Discussion Paper).
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van den Brink, R, Herings, PJJ, van der Laan, G & Talman, AJJ 2013 'The Average Tree Permission Value for Games with a Permission Tree' CentER Discussion Paper, vol. 2013-001, Econometrics, Tilburg.

The Average Tree Permission Value for Games with a Permission Tree. / van den Brink, R.; Herings, P.J.J.; van der Laan, G.; Talman, A.J.J.

Tilburg : Econometrics, 2013. (CentER Discussion Paper; Vol. 2013-001).

Research output: Working paperDiscussion paperOther research output

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AB - 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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van den Brink R, Herings PJJ, van der Laan G, Talman AJJ. The Average Tree Permission Value for Games with a Permission Tree. Tilburg: Econometrics. 2013. (CentER Discussion Paper).