The Shapley value for airport and irrigation games

Judit Márkus, Miklós Pintér and Anna Radványi

MPRA Paper from University Library of Munich, Germany

Abstract: 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).

Keywords: TU games; Shapley value; Axiomatization; Cost Sharing (search for similar items in EconPapers)
JEL-codes: C71 (search for similar items in EconPapers)
Date: 2011
New Economics Papers: this item is included in nep-cdm and nep-gth
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

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