The Average Tree Permission Value for Games with a Permission Tree

25 Pages Posted: 9 Feb 2013

See all articles by René van den Brink

René van den Brink

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

P. Jean-Jacques Herings

Tilburg University

Gerard van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics; Tinbergen Institute

Dolf Talman

Tilburg University - Department of Econometrics & Operations Research

Multiple version iconThere are 3 versions of this paper

Date Written: January 3, 2013

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.

Keywords: TU game, restricted cooperation, permission structure, Shapley value, Average Tree value, axiomatization

JEL Classification: C71

Suggested Citation

van den Brink, J.R. (René) and Herings, P. Jean-Jacques and van der Laan, Gerard and Talman, Dolf J. J., The Average Tree Permission Value for Games with a Permission Tree (January 3, 2013). Available at SSRN: https://ssrn.com/abstract=2213796 or http://dx.doi.org/10.2139/ssrn.2213796

J.R. (René) Van den Brink

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

P. Jean-Jacques Herings (Contact Author)

Tilburg University ( email )

Department of Econometrics and Operations Research
P.O. Box 90153
Tilburg, 5000 LE
Netherlands
+31 13 4668797 (Phone)
5000 LE (Fax)

HOME PAGE: http://https://sites.google.com/view/jean-jacques-herings/home

Gerard Van der Laan

Vrije Universiteit Amsterdam, School of Business and Economics ( email )

De Boelelaan 1105
Department of Econometrics and Tinbergen Institute
1081 HV Amsterdam
Netherlands

Tinbergen Institute ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

Dolf J. J. Talman

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands
+31 13 466 2346 (Phone)

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