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Profit sharing in unique Nash equilibrium: Characterization in the two-agent case

  • Leroux, Justin

Two agents jointly operate a decreasing marginal returns technology to produce a private good. We characterize the class of output-sharing rules for which the labor-supply game has a unique Nash equilibrium. It consists of two families: rules of the serial type which protect a small user from the negative externality imposed by a large user, and rules of the reverse serial type, where one agent effectively employs the other agent's labor. Exactly two rules satisfy symmetry; a result in sharp contrast with Moulin and Shenker's characterization of their serial mechanism as the unique cost-sharing rule satisfying the same incentives property [Moulin, H., Shenker, S., 1992. Serial cost sharing. Econometrica 60 (5), 1009-1037]. We also show that the familiar stand-alone test characterizes the class of fixed-path methods under our incentives criterion [Friedman, E.J., 2004. Strong monotonicity in surplus sharing. Econ. Theory 23, 643-658].

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

Volume (Year): 62 (2008)
Issue (Month): 2 (March)
Pages: 558-572

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Handle: RePEc:eee:gamebe:v:62:y:2008:i:2:p:558-572
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622836

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  1. Satterthwaite, Mark A & Sonnenschein, Hugo, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," Review of Economic Studies, Wiley Blackwell, vol. 48(4), pages 587-97, October.
  2. Friedman, Eric J., 2002. "Strategic properties of heterogeneous serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 145-154, November.
  3. Angeles de Frutos, M., 1998. "Decreasing Serial Cost Sharing under Economies of Scale," Journal of Economic Theory, Elsevier, vol. 79(2), pages 245-275, April.
  4. Alcalde, Jose & Angel Silva, Jose, 2004. "A proposal for sharing costs," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 831-845, November.
  5. Shin, Sungwhee & Suh, Sang-Chul, 1997. "Double Implementation by a Simple Game Form in the Commons Problem," Journal of Economic Theory, Elsevier, vol. 77(1), pages 205-213, November.
  6. Moulin, Herve, 2002. "Axiomatic cost and surplus sharing," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 6, pages 289-357 Elsevier.
  7. 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.
  8. Sprumont, Y., 1996. "Ordinal Cost Sharing," Cahiers de recherche 9624, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  9. Dasgupta, Partha S & Hammond, Peter J & Maskin, Eric S, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," Review of Economic Studies, Wiley Blackwell, vol. 46(2), pages 185-216, April.
  10. Leroux, Jistin, 2004. "Strategy-Proofness and Efficiency Are Incompatible in Production Economies," Working Papers 2004-07, Rice University, Department of Economics.
  11. 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.
  12. Weitzman, Martin L., 1974. "Free access vs private ownership as alternative systems for managing common property," Journal of Economic Theory, Elsevier, vol. 8(2), pages 225-234, June.
  13. Eric Friedman, 2004. "Strong monotonicity in surplus sharing," Economic Theory, Springer, vol. 23(3), pages 643-658, March.
  14. Téjédo, Cyril & Truchon, Michel, 2001. "Serial Cost Sharing in Multidimensional Contexts," Cahiers de recherche 0108, Université Laval - Département d'économique.
  15. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  16. Leroux, Justin, 2004. "Strategy-proofness and efficiency are incompatible in production economies," Economics Letters, Elsevier, vol. 85(3), pages 335-340, December.
  17. Leroux, Justin, 2005. "Strategyproof Profit Sharing in Partnerships: Improving upon Autarky," Working Papers 2005-05, Rice University, Department of Economics.
  18. Jens Leth Hougaard & Lars Thorlund-Petersen, 2000. "The stand-alone test and decreasing serial cost sharing," Economic Theory, Springer, vol. 16(2), pages 355-362.
  19. MANIQUET, François & SPRUMONT, Yves, 1998. "Efficient Strategy-Proof Allocation Functions in Linear Production Economies," Cahiers de recherche 9805, Universite de Montreal, Departement de sciences economiques.
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