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An efficient and almost budget balanced cost sharing method

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  • Moulin, Hervé

Abstract

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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Bibliographic Info

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

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Web page: http://www.elsevier.com/locate/inca/622836

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References

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  1. Justin Leroux, 2007. "Cooperative production under diminishing marginal returns: interpreting fixed-path methods," Social Choice and Welfare, Springer, vol. 29(1), pages 35-53, July.
  2. 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.
  3. Hervé Moulin, 2008. "The price of anarchy of serial, average and incremental cost sharing," Economic Theory, Springer, vol. 36(3), pages 379-405, September.
  4. 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.
  5. HervÈ CrËs & HervÈ Moulin, 2003. "Commons with increasing marginal costs: random priority versus average cost," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 44(3), pages 1097-1115, 08.
  6. Monderer, Dov & Shapley, Lloyd S., 1996. "Fictitious Play Property for Games with Identical Interests," Journal of Economic Theory, Elsevier, vol. 68(1), pages 258-265, January.
  7. Hervé Moulin & Scott Shenker, 2001. "Strategyproof sharing of submodular costs:budget balance versus efficiency," Economic Theory, Springer, vol. 18(3), pages 511-533.
  8. Manipushpak Mitra, 2001. "Mechanism design in queueing problems," Economic Theory, Springer, vol. 17(2), pages 277-305.
  9. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  10. 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.
  11. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
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Cited by:
  1. Carbajal, Juan Carlos & McLennan, Andrew & Tourky, Rabee, 2013. "Truthful implementation and preference aggregation in restricted domains," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1074-1101.

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