The Shapley value for airport and irrigation games
AbstractIn 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).
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 30031.
Date of creation: 2011
Date of revision:
TU games; Shapley value; Axiomatization; Cost Sharing;
Other versions of this item:
- Judit M rkus & Anna Radv nyi & Mikl¢s Pint‚r, 2012. "The Shapley Value for Airport and Irrigation Games," IEHAS Discussion Papers 1207, Institute of Economics, Hungarian Academy of Sciences.
- C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-04-16 (All new papers)
- NEP-CDM-2011-04-16 (Collective Decision-Making)
- NEP-GTH-2011-04-16 (Game Theory)
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