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

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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 (Econometrica, 1992) characterization of their serial mechanism as the unique cost-sharing rule satisfying the same incentives property. We also show that the familiar stand alone test characterizes the class of fixed-path methods (Friedman, Economic Theory, 2002) under our incentives criterion.

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Paper provided by HEC Montréal, Institut d'économie appliquée in its series Cahiers de recherche with number 06-11.

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Length: 19 pages
Date of creation: Oct 2006
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Handle: RePEc:iea:carech:0611

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Postal: Institut d'économie appliquée HEC Montréal 3000, Chemin de la Côte-Sainte-Catherine Montréal, Québec H3T 2A7
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Keywords: Joint production; serial rule; decreasing serial rule; strategyproofness.;

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References

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  1. 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.
  2. Leroux, Justin, 2005. "Strategyproof Profit Sharing in Partnerships: Improving upon Autarky," Working Papers 2005-05, Rice University, Department of Economics.
  3. Justin Leroux, 2006. "Cooperative production under diminishing marginal returns: Interpreting fixed-path methods," Cahiers de recherche 06-10, HEC Montréal, Institut d'économie appliquée.
  4. Leroux, Jistin, 2004. "Strategy-Proofness and Efficiency Are Incompatible in Production Economies," Working Papers 2004-07, Rice University, Department of Economics.
  5. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  6. 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.
  7. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
  8. Friedman, Eric J., 2002. "Strategic properties of heterogeneous serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 145-154, November.
  9. 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.
  10. 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.
  11. 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.
  12. 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.
  13. Téjédo, Cyril & Truchon, Michel, 2001. "Serial Cost Sharing in Multidimensional Contexts," Cahiers de recherche 0108, Université Laval - Département d'économique.
  14. Alcalde, Jose & Angel Silva, Jose, 2004. "A proposal for sharing costs," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 831-845, November.
  15. 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.
  16. Eric Friedman, 2004. "Strong monotonicity in surplus sharing," Economic Theory, Springer, vol. 23(3), pages 643-658, March.
  17. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
  18. Leroux, Justin, 2004. "Strategy-proofness and efficiency are incompatible in production economies," Economics Letters, Elsevier, vol. 85(3), pages 335-340, December.
  19. 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.
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Cited by:
  1. Carmen Beviá & Luis C. Corchón, 2007. "Cooperative Production and Efficiency," UFAE and IAE Working Papers 696.07, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
  2. Rajnish Kumar, . "Secure Implementation in Production Economies," Departmental Working Papers 2011-02, Department of Economics, Louisiana State University.

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