Comparable characterizations of four solutions for permission tree games

Rene van den Brink (), Chris Dietz (), Gerard Laan () and Genjiu Xu ()
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Chris Dietz: VU University Amsterdam
Gerard Laan: VU University Amsterdam
Genjiu Xu: Northwestern Polytechnical University

Economic Theory, 2017, vol. 63, issue 4, No 3, 903-923

Abstract: Abstract 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.

Keywords: Cooperative TU-game; Permission tree; Myerson value; Hierarchical outcome; Permission value; Axiomatization (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2017
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (8)

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DOI: 10.1007/s00199-016-0966-3

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