From hierarchies to levels: new solutions for games with hierarchical structure

M. Álvarez-Mozos, R. van den Brink, G. van der Laan, O. Tejada*

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

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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 the 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 hierarchical structure relative to that player. To define each solution, we consider a certain mapping that transforms the 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. Such transformation mappings are studied by means of properties that relate a player’s position in both types of structure.

Original languageEnglish
Pages (from-to)1089-1113
Number of pages25
JournalInternational Journal of Game Theory
Volume46
Issue number4
Early online date23 Feb 2017
DOIs
Publication statusPublished - Nov 2017

Funding

Acknowledgements Mikel Álvarez-Mozos and Oriol Tejada acknowledge the financial support of Min-isterio de Economía y Competitividad through Projects MTM2014-53395-C3-2-P and ECO2014-52340-P as well as from Generalitat de Catalunya through project 2014-SGR-40. Discussions with Hans Gersbach and Eyal Winter are acknowledged. All errors are our own.

FundersFunder number
Generalitat de Catalunya2014-SGR-40
Ministerio de Economía y CompetitividadECO2014-52340-P, MTM2014-53395-C3-2-P

    Keywords

    • Axiomatization
    • Hierarchical structure
    • Levels structure
    • Shapley value
    • TU-game

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