Comparable characterizations of four solutions for permission tree games

René van den Brink*, Chris Dietz, Gerard van der Laan, Genjiu Xu

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review


In the field of cooperative games, there is an extensive literature that studies situations of restricted cooperation. In a communication graph game, players can only cooperate if they are connected in an undirected graph representing the communication possibilities. The Myerson value of such a game is obtained by taking the Shapley value of the corresponding restricted game. For the special case that the graph is cycle-free and connected, for each player the corresponding hierarchical outcome yields an alternative solution. In a permission tree game, the player set is enriched with a rooted directed graph (or tree) on the set of players. A coalition is said to be feasible, if for every player in the coalition, except the top (root) player, also its predecessor belong(s) to the coalition. The permission value is obtained by taking the Shapley value of the associated restricted game. In this paper, we modify the Myerson value and hierarchical outcome that are defined for (undirected) communication graph games to a value for permission tree games. We also define a new solution that assigns all payoff to the unique top player in the hierarchy. Then comparable characterizations are given of these three solutions and the known permission value.

Original languageEnglish
Pages (from-to)903-923
Number of pages21
JournalEconomic Theory
Issue number4
Publication statusPublished - 1 Apr 2017


  • Axiomatization
  • Cooperative TU-game
  • Hierarchical outcome
  • Myerson value
  • Permission tree
  • Permission value


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