The Shapley Value for Airport and Irrigation Games
AbstractIn 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.
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Bibliographic InfoPaper provided by Institute of Economics, Centre for Economic and Regional Studies, Hungarian Academy of Sciences in its series IEHAS Discussion Papers with number 1207.
Length: 25 pages
Date of creation: Feb 2012
Date of revision:
Cost sharing; Shapley value; Rooted tree; Axiomatization of the Shapley value;
Other versions of this item:
- Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2012-06-13 (All new papers)
- NEP-GTH-2012-06-13 (Game Theory)
- NEP-TRE-2012-06-13 (Transport Economics)
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