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

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  • Leroux, Justin

Abstract

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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Bibliographic Info

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

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

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References

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  1. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
  2. 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.
  3. Téjédo, Cyril & Truchon, Michel, 2001. "Serial Cost Sharing in Multidimensional Contexts," Cahiers de recherche 0108, Université Laval - Département d'économique.
  4. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  5. 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.
  6. Leroux, Justin, 2004. "Strategy-proofness and efficiency are incompatible in production economies," Economics Letters, Elsevier, vol. 85(3), pages 335-340, December.
  7. 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.
  8. 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.
  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. Friedman, Eric J., 2002. "Strategic properties of heterogeneous serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 145-154, November.
  11. 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.
  12. Leroux, Jistin, 2004. "Strategy-Proofness and Efficiency Are Incompatible in Production Economies," Working Papers 2004-07, Rice University, Department of Economics.
  13. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  14. Eric Friedman, 2004. "Strong monotonicity in surplus sharing," Economic Theory, Springer, vol. 23(3), pages 643-658, March.
  15. 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).
  16. Justin Leroux, 2006. "Cooperative production under diminishing marginal returns: Interpreting fixed-path methods," Cahiers de recherche 06-10, HEC Montréal, Institut d'économie appliquée.
  17. 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.
  18. Leroux, Justin, 2005. "Strategyproof Profit Sharing in Partnerships: Improving upon Autarky," Working Papers 2005-05, Rice University, Department of Economics.
  19. Alcalde, Jose & Angel Silva, Jose, 2004. "A proposal for sharing costs," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 831-845, November.
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Cited by:
  1. Carmen Bevia & Luis C. Corchon, 2007. "Cooperative production and efficiency," Economics Working Papers we070502, Universidad Carlos III, Departamento de Economía.
  2. Kumar, Rajnish, 2013. "Secure implementation in production economies," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 372-378.

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