From hierarchies to levels: New solutions for games with hierarchical structure
Open access
Date
2015-05Type
- Working Paper
ETH Bibliography
yes
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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 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 anaxiomatic viewpoint by means of properties that relate a player’s position in both types of structure. Show more
Permanent link
https://doi.org/10.3929/ethz-a-010437029Publication status
publishedJournal / series
Economics Working Paper SeriesVolume
Publisher
ETH Zurich, Center of Economic Research (CER-ETH)Subject
TU-game; Hierarchical structure; Levels structure; Shapley Value; AxiomatizationOrganisational unit
02045 - Dep. Geistes-, Sozial- u. Staatswiss. / Dep. of Humanities, Social and Pol.Sc.03729 - Gersbach, Hans / Gersbach, Hans
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Is previous version of: https://doi.org/10.3929/ethz-b-000227707
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ETH Bibliography
yes
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