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An efficient and almost budget balanced cost sharing method

  • Moulin, Hervé

For a convex technology C we characterize cost sharing games where the Nash equilibrium demands maximize total surplus. Budget balance is possible if and only if C is polynomial of degree n-1 or less. For general C, the residual* cost shares are balanced if at least one demand is null, a characteristic property. If the cost function is totally monotone, a null demand receives cash and total payments may exceed actual cost. The ratio of excess payment to efficient surplus is at most . For power cost functions, C(a)=ap, p>1, the ratio of budget imbalance to efficient surplus vanishes as . For analytic cost functions, the ratio converges to zero exponentially along a given sequence of users. All asymptotic properties are lost if the cost function is not smooth.

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Article provided by Elsevier in its journal Games and Economic Behavior.

Volume (Year): 70 (2010)
Issue (Month): 1 (September)
Pages: 107-131

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Handle: RePEc:eee:gamebe:v:70:y:2010:i:1:p:107-131
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Justin Leroux, 2006. "Cooperative production under diminishing marginal returns: Interpreting fixed-path methods," Cahiers de recherche 06-10, HEC Montréal, Institut d'économie appliquée.
  2. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer, vol. 36(3), pages 379-405, September.
  3. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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  5. Moulin, Herve & Cres, Herve, 2000. "Commons with Increasing Marginal Costs: Random Priority versus Average Cost," Working Papers 2000-04, Rice University, Department of Economics.
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  7. Kukushkin, Nikolai S., 2004. "Best response dynamics in finite games with additive aggregation," Games and Economic Behavior, Elsevier, vol. 48(1), pages 94-110, July.
  8. Luis Corchón & M. Socorro Puy, 2000. "- Existence And Nash Implementation Of Efficient Sharing Rules For A Commonly Owned Technology," Working Papers. Serie AD 2000-03, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  9. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer, vol. 18(3), pages 511-533.
  10. Luis C. Corchón & M. Socorro Puy, 2002. "Existence and Nash implementation of efficient sharing rules for a commonly owned technology," Social Choice and Welfare, Springer, vol. 19(2), pages 369-379, April.
  11. Ruben Juarez, 2008. "The worst absolute surplus loss in the problem of commons: random priority versus average cost," Economic Theory, Springer, vol. 34(1), pages 69-84, January.
  12. Watts, Alison, 1996. "On the Uniqueness of Equilibrium in Cournot Oligopoly and Other Games," Games and Economic Behavior, Elsevier, vol. 13(2), pages 269-285, April.
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