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Contracts, cost sharing and consistency

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  • Koster, M.

    () (University of Amsterdam)

Abstract

Under a contract, agents are not only held to honor the allocation as prescribed by a cost sharing mechanism but also a full description of allocated units and costs once production falls short. For agents leaving the cost sharing problem by taking their demanded units and prepaying the corresponding bill, a contract allows for a reformulation of the cost sharing problem to serve the remaining agents. Consistency requires invariance of cost shares relative to any such reduced cost sharing problem. Under consistency, the proportional mechanisms uniquely satisfy additivity and positivity of cost shares. Exchanging positivity by equal treatment characterizes the set of mechanisms which propose proportional shares for only those agents in the maximal indifference set for some preordering on the rest of nonnegative numbers. This includes egalitarian and average cost sharing. The latter is further characterized by the properties linearity. Under R-consistency, a mechanism is supported by at least one reasonable contract, which meets upperbounds. The class of additive and R-consistent mechanisms is isomorphic to the class of consistent and monotonic rationing methods. Consequently serial cost sharing is R-consistent, whereas Shapley-Shubik is not. Examples are given how the extensive literature on consistent monotonic rationing can be inferred to study and characterize cost sharing mechanisms.

Suggested Citation

  • Koster, M., 2009. "Contracts, cost sharing and consistency," CeNDEF Working Papers 09-04, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.
  • Handle: RePEc:ams:ndfwpp:09-04
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    References listed on IDEAS

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    1. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
    2. Oscar Volij & Nir Dagan, 1997. "Bilateral Comparisons and Consistent Fair Division Rules in the Context of Bankruptcy Problems," International Journal of Game Theory, Springer;Game Theory Society, vol. 26(1), pages 11-25.
    3. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    4. Robert J. Weber, 1977. "Probabilistic Values for Games," Cowles Foundation Discussion Papers 471R, Cowles Foundation for Research in Economics, Yale University.
    5. Trudeau, Christian, 2009. "Cost sharing with multiple technologies," Games and Economic Behavior, Elsevier, vol. 67(2), pages 695-707, November.
    6. Sharkey,William W., 1983. "The Theory of Natural Monopoly," Cambridge Books, Cambridge University Press, number 9780521271943.
    7. Thomson, William, 2008. "The two-agent claims-truncated proportional rule has no consistent extension: A constructive proof," Economics Letters, Elsevier, vol. 98(1), pages 59-65, January.
    8. Albizuri, M. Josune & Zarzuelo, Jose M., 2007. "The dual serial cost-sharing rule," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 150-163, March.
    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. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    11. William Thomson, 2001. "On the axiomatic method and its recent applications to game theory and resource allocation," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(2), pages 327-386.
    12. Hougaard, Jens Leth & Thorlund-Petersen, Lars, 2001. "Mixed serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 51-68, January.
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    Cited by:

    1. Maurice Koster, 2012. "Consistent cost sharing," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 75(1), pages 1-28, February.
    2. repec:spr:compst:v:75:y:2012:i:1:p:1-28 is not listed on IDEAS

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