The Shapley Value for Airport and Irrigation Games

Judit Markus, Anna Radvanyi () and Miklos Pinter ()
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Judit Markus: Corvinus University of Budapest
Anna Radvanyi: Department of Mathematics, Corvinus University of Budapest
Miklos Pinter: Department of Mathematics, Corvinus University of Budapest

No 1207, CERS-IE WORKING PAPERS from Institute of Economics, Centre for Economic and Regional Studies

Abstract: In this paper cost sharing problems are considered. We focus on problems on a rooted tree, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, we call these games 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 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 on a rooted tree. In our characterization results we relate the TU games terminologies to the cost sharing terminologies, so we bridge between the two fields.

Keywords: Cost sharing; Shapley value; Rooted tree; Axiomatization of the Shapley value (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Pages: 25 pages
Date: 2012-02
New Economics Papers: this item is included in nep-gth and nep-tre
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Citations: View citations in EconPapers (4)

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