From Hierarchies to Levels: New Solutions for Games

Tinbergen Institute Discussion Paper 15-072/II

49 Pages Posted: 2 Jun 2015

See all articles by Mikel Alvarez-Mozos

Mikel Alvarez-Mozos

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics

René van den Brink

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

Gerard van der Laan

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

Oriol Tejada

ETH Zürich - CER-ETH - Center of Economic Research at ETH Zurich

Date Written: June 2, 2015

Abstract

Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the structure relative to that player. To define each of these solutions, we consider a certain mapping that transforms any hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley Value to the class of games with levels structure. The transformations that map the set of hierarchical structures to the set of levels structures are also studied from an axiomatic viewpoint by means of properties that relate a player’s position in both types of structure.

Keywords: TU-game; hierarchical structure; levels structure; Shapley Value; axiomatization

JEL Classification: C71

Suggested Citation

Alvarez-Mozos, Mikel and van den Brink, J.R. (René) and van der Laan, Gerard and Tejada, Oriol, From Hierarchies to Levels: New Solutions for Games (June 2, 2015). Tinbergen Institute Discussion Paper 15-072/II. Available at SSRN: https://ssrn.com/abstract=2613316 or http://dx.doi.org/10.2139/ssrn.2613316

Mikel Alvarez-Mozos (Contact Author)

University of Barcelona - Department of Actuarial, Financial and Economic Mathematics ( email )

Avda. Diagonal 690
Barcelona, 08034
Spain

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

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

Oriol Tejada

ETH Zürich - CER-ETH - Center of Economic Research at ETH Zurich ( email )

Zürichbergstrasse 18
Zurich, 8092
Switzerland
41446329693 (Phone)

HOME PAGE: http://www.cer.ethz.ch/mip/people/toriol

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