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The Shapley Value for Airport and Irrigation Games

Author

Listed:
  • Judit Markus

    (Corvinus University of Budapest)

  • Anna Radvanyi

    (Department of Mathematics, Corvinus University of Budapest)

  • Miklos Pinter

    (Department of Mathematics, Corvinus University of Budapest)

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.

Suggested Citation

  • Judit Markus & Anna Radvanyi & Miklos Pinter, 2012. "The Shapley Value for Airport and Irrigation Games," CERS-IE WORKING PAPERS 1207, Institute of Economics, Centre for Economic and Regional Studies.
    • Handle: RePEc:has:discpr:1207
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    Citations

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    Cited by:

    1. Gillman, Max, 2012. "AS-AD in the Standard Dynamic Neoclassical Model: Business Cycles and Growth Trends," Cardiff Economics Working Papers E2012/12, Cardiff University, Cardiff Business School, Economics Section.
    2. Zsolt Darvas, 2013. "Monetary transmission in three central European economies: evidence from time-varying coefficient vector autoregressions," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 40(2), pages 363-390, May.
    3. Magdolna Sass & Miklos Szanyi, 2012. "Two essays on Hungarian relocations," CERS-IE WORKING PAPERS 1223, Institute of Economics, Centre for Economic and Regional Studies.
    4. Andras Simonovits, 2012. "Means-tested or Flat Pension? Pension Credit," CERS-IE WORKING PAPERS 1221, Institute of Economics, Centre for Economic and Regional Studies.

    More about this item

    Keywords

    Cost sharing; Shapley value; Rooted tree; Axiomatization of the Shapley value;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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