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The Shapley value for airport and irrigation games

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  • Márkus, Judit
  • Pintér, Miklós
  • Radványi, Anna

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).

Suggested Citation

  • Márkus, Judit & Pintér, Miklós & Radványi, Anna, 2011. "The Shapley value for airport and irrigation games," MPRA Paper 30031, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:30031
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    References listed on IDEAS

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    1. Nimrod Megiddo, 1978. "Computational Complexity of the Game Theory Approach to Cost Allocation for a Tree," Mathematics of Operations Research, INFORMS, vol. 3(3), pages 189-196, August.
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    8. S. H. Tijs & M. Koster & E. Molina & Y. Sprumont, 2002. "Sharing the cost of a network: core and core allocations," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(4), pages 567-599.
    9. Bezalel Peleg & Peter Sudhölter, 2007. "Introduction to the Theory of Cooperative Games," Theory and Decision Library C, Springer, edition 0, number 978-3-540-72945-7, December.
    10. William Thomson, 2007. "Cost allocation and airport problems," RCER Working Papers 537, University of Rochester - Center for Economic Research (RCER).
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    Cited by:

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    2. Max Gillman, 2012. "AS-AD in the Standard Dynamic Neoclassical Model: Business Cycles and Growth Trends," CERS-IE WORKING PAPERS 1222, Institute of Economics, Centre for Economic and Regional Studies.
    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. Thomson, William, 2024. "Cost allocation and airport problems," Mathematical Social Sciences, Elsevier, vol. 131(C), pages 17-31.

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    More about this item

    Keywords

    TU games; Shapley value; Axiomatization; Cost Sharing;
    All these keywords.

    JEL classification:

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

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