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A Discrete Cost Sharing Model with Technological Cooperation

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  • Eric Bahel
  • Christian Trudeau

Abstract

This paper proposes a setting that allows for technological cooperation in the cost sharing model. Dealing with discrete demands, we study two properties: Additivity and Dummy. We show that these properties are insuffcient to guarantee a unit-flow representation similar to that of Wang (1999). To obtain a characterization of unit flows, we strengthen the Dummy axiom and introduce a property that requires the cost share of every agent to be nondecreasing in the incremental costs generated by their demand. Finally, a fairness requirement as to the compensation of technological cooperation is examined.

Suggested Citation

  • Eric Bahel & Christian Trudeau, 2011. "A Discrete Cost Sharing Model with Technological Cooperation," Working Papers e07-28, Virginia Polytechnic Institute and State University, Department of Economics.
  • Handle: RePEc:vpi:wpaper:e07-28
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    File URL: ftp://repec.econ.vt.edu/Papers/Bahel/sharing_techno.pdf
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    References listed on IDEAS

    as
    1. Yves Sprumont, 2005. "On the Discrete Version of the Aumann-Shapley Cost-Sharing Method," Econometrica, Econometric Society, vol. 73(5), pages 1693-1712, September.
    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. Bergantinos, Gustavo & Vidal-Puga, Juan J., 2007. "A fair rule in minimum cost spanning tree problems," Journal of Economic Theory, Elsevier, vol. 137(1), pages 326-352, November.
    4. Eric J. Friedman, 2004. "Paths and consistency in additive cost sharing," International Journal of Game Theory, Springer;Game Theory Society, vol. 32(4), pages 501-518, August.
    5. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
    6. Jackson, Matthew O., 2005. "Allocation rules for network games," Games and Economic Behavior, Elsevier, pages 128-154.
    7. Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, pages 152-188.
    8. Moulin, Herve & Sprumont, Yves, 2005. "On demand responsiveness in additive cost sharing," Journal of Economic Theory, Elsevier, pages 1-35.
    9. Friedman, Eric & Moulin, Herve, 1999. "Three Methods to Share Joint Costs or Surplus," Journal of Economic Theory, Elsevier, pages 275-312.
    10. Hsiao Chih-Ru & Raghavan T. E. S., 1993. "Shapley Value for Multichoice Cooperative Games, I," Games and Economic Behavior, Elsevier, vol. 5(2), pages 240-256, April.
    11. Wang, YunTong, 1999. "The additivity and dummy axioms in the discrete cost sharing model," Economics Letters, Elsevier, vol. 64(2), pages 187-192, August.
    12. Jelnov, Artyom & Tauman, Yair, 2009. "The private value of a patent: A cooperative approach," Mathematical Social Sciences, Elsevier, vol. 58(1), pages 84-97, July.
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    Citations

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    Cited by:

    1. Trudeau, Christian, 2014. "Minimum cost spanning tree problems with indifferent agents," Games and Economic Behavior, Elsevier, vol. 84(C), pages 137-151.
    2. 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.
    3. Bahel, Eric & Trudeau, Christian, 2014. "Stable lexicographic rules for shortest path games," Economics Letters, Elsevier, pages 266-269.
    4. Eric Bahel & Christian Trudeau, 2014. "Stable cost sharing in production allocation games," Working Papers 1402, University of Windsor, Department of Economics.
    5. Albizuri, M.J. & Díez, H. & Sarachu, A., 2014. "Monotonicity and the Aumann–Shapley cost-sharing method in the discrete case," European Journal of Operational Research, Elsevier, vol. 238(2), pages 560-565.
    6. Bahel, Eric & Haller, Hans, 2013. "Cycles with undistinguished actions and extended Rock–Paper–Scissors games," Economics Letters, Elsevier, pages 588-591.

    More about this item

    Keywords

    cost sharing; demand; technology; cooperation; fow methods;

    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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