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Cost Sharing in Chains and Other Fixed Trees

Author

Listed:
  • Hougaard, Jens Leth

    () (Department of Food and Resource Economics)

  • Tvede, Mich

    () (Newcastle University)

  • Østerdal, Lars Peter

    () (Department of Business and Economics)

Abstract

We consider a cost sharing problem among agents on a line. The problem is closely related to the classic airport game, but in our model agents are characterized by their location, rather than their needed runway length. We characterize a family of cost allocation rules in which agents pay a share of the incremental costs as well as any debt from upstream agents, with the Bird rule (where agents pay their full incremental cost) and the ‘free rider’ rule (where the terminal agent pays everything) as the two extreme cases. We also extend the analysis to cost sharing among agents located on a fixed tree structure.

Suggested Citation

  • Hougaard, Jens Leth & Tvede, Mich & Østerdal, Lars Peter, 2013. "Cost Sharing in Chains and Other Fixed Trees," Discussion Papers of Business and Economics 12/2013, University of Southern Denmark, Department of Business and Economics.
  • Handle: RePEc:hhs:sdueko:2013_012
    as

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    File URL: https://www.sdu.dk/-/media/files/om_sdu/institutter/ivoe/disc_papers/disc_2013/dpbe12_2013.pdf
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    References listed on IDEAS

    as
    1. Potters, Jos & Sudholter, Peter, 1999. "Airport problems and consistent allocation rules," Mathematical Social Sciences, Elsevier, vol. 38(1), pages 83-102, July.
    2. Rodica Brânzei & Elena Iñarra & Stef Tijs & José Zarzuelo, 2006. "A Simple Algorithm for the Nucleolus of Airport Profit Games," International Journal of Game Theory, Springer;Game Theory Society, vol. 34(2), pages 259-272, August.
    3. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    4. Aadland, David & Kolpin, Van, 1998. "Shared irrigation costs: An empirical and axiomatic analysis," Mathematical Social Sciences, Elsevier, vol. 35(2), pages 203-218, March.
    5. S.C. Littlechild & G.F. Thompson, 1977. "Aircraft Landing Fees: A Game Theory Approach," Bell Journal of Economics, The RAND Corporation, vol. 8(1), pages 186-204, Spring.
    6. S. C. Littlechild & G. Owen, 1973. "A Simple Expression for the Shapley Value in a Special Case," Management Science, INFORMS, vol. 20(3), pages 370-372, November.
    7. Granot, D & Maschler, M & Owen, G & Zhu, W.R., 1996. "The Kernel/Nucleolus of a Standard Tree Game," International Journal of Game Theory, Springer;Game Theory Society, vol. 25(2), pages 219-244.
    8. J. Barkley Rosser, 2009. "Introduction," Chapters,in: Handbook of Research on Complexity, chapter 1 Edward Elgar Publishing.
    9. William Thomson, 2007. "Cost allocation and airport problems," RCER Working Papers 537, University of Rochester - Center for Economic Research (RCER).
    10. Sharkey, W.W., 1991. "Network Models in Economics," Papers 69, Bell Communications - Economic Research Group.
    11. Pradeep Dubey, 1982. "The Shapley Value as Aircraft Landing Fees--Revisited," Management Science, INFORMS, vol. 28(8), pages 869-874, August.
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    More about this item

    Keywords

    Airport game; cost allocation; axiomatic characterization; Bird Rule; Incremental cost sharing;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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