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Games on Union Closed Systems

Tinbergen Institute Discussion Paper 11-036/1

24 Pages Posted: 16 Feb 2011  

René van den Brink

VU University Amsterdam - Department of Economics; Tinbergen Institute; Tinbergen Institute - Tinbergen Institute Amsterdam (TIA)

Ilya V. Katsev

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

Gerard van der Laan

VU University Amsterdam - Faculty of Economics and Business Administration; Tinbergen Institute - Tinbergen Institute Amsterdam (TIA)

Date Written: February 11, 2011

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 solution for TU-games assigns a set of payoff distributions to every TU-game. 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. Properties of solutions (the core, the nucleolus, the prekernel and the Shapley value) are given for games on union closed systems.

Keywords: TU-game, restricted cooperation, union closed system, core, prekernel, nucleolus

JEL Classification: C71

Suggested Citation

van den Brink, René and Katsev, Ilya V. and van der Laan, Gerard, Games on Union Closed Systems (February 11, 2011). Tinbergen Institute Discussion Paper 11-036/1. Available at SSRN: https://ssrn.com/abstract=1761942 or http://dx.doi.org/10.2139/ssrn.1761942

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 - Tinbergen Institute Amsterdam (TIA) ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
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

VU University Amsterdam - Faculty of Economics and Business Administration ( email )

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

Tinbergen Institute - Tinbergen Institute Amsterdam (TIA) ( email )

Gustav Mahlerplein 117
Amsterdam, 1082 MS
Netherlands

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