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

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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File URL: http://www.hec.ca/iea/cahiers/2006/iea0611_jleroux.pdf
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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
Date of revision:
Handle: RePEc:iea:carech:0611
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  1. Cyril Téjédo & Michel Truchon, 2001. "Serial Cost Sharing in Multidimensional Contexts," Cahiers de recherche 01-07, Departement d'Economique de la Faculte d'administration à l'Universite de Sherbrooke.
  2. Justin Leroux, 2006. "Cooperative production under diminishing marginal returns: Interpreting fixed-path methods," Cahiers de recherche 06-10, HEC Montréal, Institut d'économie appliquée.
  3. Alcalde, Jose & Angel Silva, Jose, 2004. "A proposal for sharing costs," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 831-845, November.
  4. Leroux, Jistin, 2004. "Strategy-Proofness and Efficiency Are Incompatible in Production Economies," Working Papers 2004-07, Rice University, Department of Economics.
  5. François Maniquet & Yves Sprumont, 1999. "Efficient strategy-proof allocation functions in linear production economies," Economic Theory, Springer, vol. 14(3), pages 583-595.
  6. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
  7. 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.
  8. Leroux, Justin, 2004. "Strategy-proofness and efficiency are incompatible in production economies," Economics Letters, Elsevier, vol. 85(3), pages 335-340, December.
  9. Friedman, Eric J., 2002. "Strategic properties of heterogeneous serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 145-154, November.
  10. 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.
  11. 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.
  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. 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.
  14. Moulin, Herve, 2001. "Axiomatic Cost and Surplis-Sharing," Working Papers 2001-06, Rice University, Department of Economics.
  15. 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.
  16. 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.
  17. Eric Friedman, 2004. "Strong monotonicity in surplus sharing," Economic Theory, Springer, vol. 23(3), pages 643-658, March.
  18. Leroux, Justin, 2005. "Strategyproof Profit Sharing in Partnerships: Improving upon Autarky," Working Papers 2005-05, Rice University, Department of Economics.
  19. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-37, September.
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