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Sharing Variable Returns of Cooperation


  • Koster, M.

    () (Universiteit van Amsterdam)


A finite set of agents jointly undertake a project. Depending on the aggregate of individual agent characteristics the project runs losses or profits, which have to be shared. This paper adopts the mechanistic view and concentrates on devices that a contingent planner may use in order to share the net profits. The Moulin and Shenker (1994) representation theorem is used to show that additive mechanisms with the constant returns property relate 1 to 1 to rationing methods. Refinements are discussed dealing with monotonicity and equity properties that relate to the dispersion of shares. The second part introduces the notion of a consistent solution. Each rationing method induced by a consistent mechanism is consistent. If such mechanism is continuous as well, then the corresponding rationing method is parametric in the terminology of Young (1998) and Moulin (2000). Most prevalent mechanisms (average, serial, Shapley-Shubik) are consistent as member of the class of incremental mechanisms. Each interval consistent incremental mechanism is shown to be a composition of marginal mechanisms and the average mechanism. Immediately the average mechanism is the unique strongly consistent solution. Finally a characterization of mechanisms within the general class is discussed using super-additivity.

Suggested Citation

  • Koster, M., 2005. "Sharing Variable Returns of Cooperation," CeNDEF Working Papers 05-06, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:05-06

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    References listed on IDEAS

    1. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    2. Moulin Herve & Shenker Scott, 1994. "Average Cost Pricing versus Serial Cost Sharing: An Axiomatic Comparison," Journal of Economic Theory, Elsevier, vol. 64(1), pages 178-201, October.
    3. Eric Friedman, 1997. "Weak and Strong Consistency in Additive Cost Sharing," Departmental Working Papers 199707, Rutgers University, Department of Economics.
    4. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    5. Sudholter, Peter, 1998. "Axiomatizations of Game Theoretical Solutions for One-Output Cost Sharing Problems," Games and Economic Behavior, Elsevier, vol. 24(1-2), pages 142-171, July.
    6. Young, H.P., 1994. "Cost allocation," Handbook of Game Theory with Economic Applications,in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 2, chapter 34, pages 1193-1235 Elsevier.
    7. Thomson, W., 1996. "Consistent Allocation Rules," RCER Working Papers 418, University of Rochester - Center for Economic Research (RCER).
    8. Aumann, Robert J. & Maschler, Michael, 1985. "Game theoretic analysis of a bankruptcy problem from the Talmud," Journal of Economic Theory, Elsevier, vol. 36(2), pages 195-213, August.
    9. Martin Shubik, 1962. "Incentives, Decentralized Control, the Assignment of Joint Costs and Internal Pricing," Management Science, INFORMS, vol. 8(3), pages 325-343, April.
    10. Tijs, S.H. & Koster, M.A.L., 1998. "General aggregation of demand and cost sharing methods," Other publications TiSEM 43bb1596-ff5b-4567-a25f-9, Tilburg University, School of Economics and Management.
    11. Hougaard, Jens Leth & Thorlund-Petersen, Lars, 2001. "Mixed serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 51-68, January.
    12. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
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