Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems

Tinbergen Institute Discussion Paper 09-064/1

22 Pages Posted: 17 Jul 2009

See all articles by René van den Brink

René van den Brink

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

Ilya V. Katsev

Russian Academy of Sciences (RAS) - Saint Petersburg Institute for Economics and Mathmatics

Gerard van der Laan

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

Date Written: July 17, 2009

Abstract

A situation in which a finite set of players can obtain certain payoffs by cooperation can be described by a cooperative game with transferable utility, or simply a TU-game. A (single-valued) solution for TU-games assigns a payoff distribution to every TU-game. A well-known solution is the Shapley value. In the literature various models of games with restricted cooperation can be found. So, instead of allowing all subsets of the player set N to form, it is assumed that the set of feasible coalitions is a subset of the power set of N. In this paper we consider such sets of feasible coalitions that are closed under union, i.e. for any two feasible coalitions also their union is feasible. We consider and axiomatize two solutions or rules for these games that generalize the Shapley value: one is obtained as the conjunctive permission value using a corresponding superior graph, the other is defined as the Shapley value of a modified game similar as the Myerson rule for conference structures.

Keywords: TU-game, restricted cooperation, union closed system, Shapley value, permission value, superior graph, axiomatization

JEL Classification: C71

Suggested Citation

van den Brink, J.R. (René) and Katsev, Ilya V. and van der Laan, Gerard, Axiomatizations of Two Types of Shapley Values for Games on Union Closed Systems (July 17, 2009). Tinbergen Institute Discussion Paper 09-064/1, Available at SSRN: https://ssrn.com/abstract=1435331 or http://dx.doi.org/10.2139/ssrn.1435331

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

Ilya V. Katsev

Russian Academy of Sciences (RAS) - Saint Petersburg Institute for Economics and Mathmatics ( email )

Tchaikovsky st. 1
Saint Petersburg, 191187
Russia

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

Do you have negative results from your research you’d like to share?

Paper statistics

Downloads
59
Abstract Views
613
Rank
648,767
PlumX Metrics