# 12-126/II (2012-11-27)

Rene van den Brink, VU University Amsterdam; Chris Dietz, VU University Amsterdam
Cooperative TU-game, peer group game, digraph game, game with a permission structure, local permission structure
JEL codes:

This discussion paper resulted in a publication in 'Theory and Decision', 2014, 76, 343-361.

It is known that peer group games are a special class of games with a permission structure. However, peer group games are also a special class of (weighted) digraph games. To be specific, they are digraph games in which the digraph is the transitive closure of a rooted tree. In this paper we first argue that some known results on solutions for peer group games hold more general for digraph games. Second, we generalize both digraph games as well as games with a permission structure into a model called games with a local permission structure, where every player needs permission from its predecessors only in order to generate worth, but does not need its predecessors in order to give permission to its own successors. We introduce and axiomatize a Shapley value type solution for these games, generalizing the conjunctive permission value for games with a permission structure and the beta-measure for weighted digraphs.