Games with a Local Permission Structure: Separation of Authority and Value Generation

Tinbergen Institute Discussion Paper 12-126/II

26 Pages Posted: 27 Nov 2012

See all articles by René van den Brink

René van den Brink

VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute

Chris Dietz

VU University Amsterdam

Date Written: November 23, 2012

Abstract

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.

Keywords: Cooperative TU-game, peer group game, digraph game, game with a permission structure, local permission structure

JEL Classification: C71

Suggested Citation

van den Brink, J.R. (René) and Dietz, Chris, Games with a Local Permission Structure: Separation of Authority and Value Generation (November 23, 2012). Tinbergen Institute Discussion Paper 12-126/II, Available at SSRN: https://ssrn.com/abstract=2181446 or http://dx.doi.org/10.2139/ssrn.2181446

J.R. (René) Van den Brink (Contact Author)

VU University Amsterdam - Department of Economics ( email )

De Boelelaan 1105
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Tinbergen Institute ( email )

Burg. Oudlaan 50
Rotterdam, 3062 PA
Netherlands

Chris Dietz

VU University Amsterdam ( email )

De Boelelaan 1105
Amsterdam, ND North Holland 1081 HV
Netherlands

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