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 language | English |
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Pages (from-to) | 1089-1113 |
Number of pages | 25 |
Journal | International Journal of Game Theory |
Volume | 46 |
Issue number | 4 |
Early online date | 23 Feb 2017 |
DOIs | |
Publication status | Published - 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.
Funders | Funder number |
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Generalitat de Catalunya | 2014-SGR-40 |
Ministerio de Economía y Competitividad | ECO2014-52340-P, MTM2014-53395-C3-2-P |
Keywords
- Axiomatization
- Hierarchical structure
- Levels structure
- Shapley value
- TU-game