The Shapley value for airport and irrigation games

Pintér, Miklós and Radványi, Anna and Márkus, Judit (2011) The Shapley value for airport and irrigation games. Working Paper. Corvinus University of Budapest. (Unpublished)

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In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games Littlechild and Thompson (1977) is a subclass of irrigation games. The Shapley value Shapley (1953) is probably the most popular solution concept for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's Shapley (1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irrigation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. We also note that for irrigation games the Shapley value is always stable, that is it is always in the core Gillies (1959).

Item Type:Monograph (Working Paper)
Uncontrolled Keywords:TU games, Shapley value, axiomatization, cost sharing
Subjects:Mathematics, Econometrics
Projects:OTKA 72856
ID Code:552
Deposited By: Ádám Hoffmann
Deposited On:08 Mar 2012 16:36
Last Modified:18 Oct 2021 08:59

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