Computation of the Nucleolus for a Class of Disjunctive Games with a Permission Structure

Tinbergen Institute Dissusion Paper No. TI 08-060/1

30 Pages Posted: 24 Jun 2008

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: June, 23 2008

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 nucleolus. A cooperative game with a permission structure describes a situation in which players in a cooperative TU-game are hierarchically ordered in the sense that there are players that need permission from other players before they are allowed to cooperate. The corresponding restricted game takes account of the limited cooperation possibilities by assigning to every coalition the worth of its largest feasible subset. In this paper we provide a polynomial time algorithm for computing the nucleolus of the restricted games corresponding to a class of games with permission structure.

Keywords: TU-game, nucleolus, game with permission structure, peer group game, information market game, algorithm, complexity

JEL Classification: C71

Suggested Citation

van den Brink, J.R. (René) and Katsev, Ilya V. and van der Laan, Gerard, Computation of the Nucleolus for a Class of Disjunctive Games with a Permission Structure (June, 23 2008). Tinbergen Institute Dissusion Paper No. TI 08-060/1, Available at SSRN: https://ssrn.com/abstract=1150065 or http://dx.doi.org/10.2139/ssrn.1150065

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

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