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Independence of dummy units and Shapley-Shubik methods in cost sharing problems with technological cooperation

Author

Listed:
  • Eric Bahel

    () (Department of Economics, Virginia Polytechnic Institute and State University)

  • Christian Trudeau

    () (Department of Economics, University of Windsor)

Abstract

In the discrete cost sharing model with technological cooperation (Bahel and Trudeau (IJGT, 2013)), we study the implications of a number of properties that strengthen the well-known Dummy axiom. Our main axiom, which requires that costless units of demands do not affect the cost shares, is used to characterize two classes of rules. Combined with anonymity and a specific stability property, this requirement picks up sharing methods that allow the full compensation of at most one technological contribution. If instead we strengthen the well-known Dummy property to include agents whose technological contribution is offset by the cost of their demand, we are left with an adaptation of the Shapley-Shubik method that treats technologies as private and rewards their contributions. Our results provide two interesting axiomatizations for the adaptations of the Shapley-Shubik rule to our framework.

Suggested Citation

  • Eric Bahel & Christian Trudeau, 2013. "Independence of dummy units and Shapley-Shubik methods in cost sharing problems with technological cooperation," Working Papers 1304, University of Windsor, Department of Economics.
  • Handle: RePEc:wis:wpaper:1304
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    File URL: http://web2.uwindsor.ca/economics/RePEc/wis/pdf/1304.pdf
    File Function: First version, 2013
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    References listed on IDEAS

    as
    1. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
    2. Hervé Moulin, 1995. "On Additive Methods To Share Joint Costs," The Japanese Economic Review, Japanese Economic Association, vol. 46(4), pages 303-332, December.
    3. Yves Sprumont, 2008. "Nearly serial sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 37(2), pages 155-184, June.
    4. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, pages 7-36.
    5. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, pages 1-35.
    6. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, pages 325-343.
    7. Eric Bahel & Christian Trudeau, 2013. "A discrete cost sharing model with technological cooperation," International Journal of Game Theory, Springer;Game Theory Society, pages 439-460.
    8. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, pages 325-343.
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    More about this item

    Keywords

    Shapley-Shubik; Technological Cooperation; Dummy;

    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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