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

Mikel Álvarez-Mozos, R. Brink, G. Laan and Oriol Tejada
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R. Brink: VU Amsterdam
G. Laan: VU Amsterdam

International Journal of Game Theory, 2017, vol. 46, issue 4, No 10, 1089-1113

Abstract: 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.

Keywords: TU-game; Hierarchical structure; Levels structure; Shapley value; Axiomatization (search for similar items in EconPapers)
JEL-codes: C7 C70 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (8)

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Working Paper: From Hierarchies to Levels: New Solutions for Games with Hierarchical Structure (2015)
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DOI: 10.1007/s00182-017-0572-z

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