IDEAS home Printed from https://ideas.repec.org/a/eee/gamebe/v62y2008i2p558-572.html
   My bibliography  Save this article

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

Author

Listed:
  • 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].

Suggested Citation

  • Leroux, Justin, 2008. "Profit sharing in unique Nash equilibrium: Characterization in the two-agent case," Games and Economic Behavior, Elsevier, vol. 62(2), pages 558-572, March.
    • Handle: RePEc:eee:gamebe:v:62:y:2008:i:2:p:558-572
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0899-8256(07)00079-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. 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.
    2. 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.
    3. Amartya K. Sen, 1966. "Labour Allocation in a Cooperative Enterprise," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 33(4), pages 361-371.
    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;Society for the Advancement of Economic Theory (SAET), vol. 14(3), pages 583-595.
    6. Justin Leroux, 2007. "Cooperative production under diminishing marginal returns: interpreting fixed-path methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 35-53, July.
    7. Alcalde, Jose & Angel Silva, Jose, 2004. "A proposal for sharing costs," Journal of Mathematical Economics, Elsevier, vol. 40(7), pages 831-845, November.
    8. Tejedo, Cyril & Truchon, Michel, 2002. "Serial cost sharing in multidimensional contexts," Mathematical Social Sciences, Elsevier, vol. 44(3), pages 277-299, December.
    9. Sprumont, Yves, 1998. "Ordinal Cost Sharing," Journal of Economic Theory, Elsevier, vol. 81(1), pages 126-162, July.
    10. 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;The Society for Social Choice and Welfare, vol. 19(2), pages 369-379.
    11. Moulin, Herve & Shenker, Scott, 1992. "Serial Cost Sharing," Econometrica, Econometric Society, vol. 60(5), pages 1009-1037, September.
    12. Jens Leth Hougaard & Lars Thorlund-Petersen, 2000. "The stand-alone test and decreasing serial cost sharing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 16(2), pages 355-362.
    13. Mark A. Satterthwaite & Hugo Sonnenschein, 1981. "Strategy-Proof Allocation Mechanisms at Differentiable Points," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 48(4), pages 587-597.
    14. Partha Dasgupta & Peter Hammond & Eric Maskin, 1979. "The Implementation of Social Choice Rules: Some General Results on Incentive Compatibility," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 46(2), pages 185-216.
    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. Friedman, Eric J., 2002. "Strategic properties of heterogeneous serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 44(2), pages 145-154, November.
    17. Leroux, Justin, 2005. "Strategyproof Profit Sharing in Partnerships: Improving upon Autarky," Working Papers 2005-05, Rice University, Department of Economics.
    18. Eric Friedman, 2004. "Strong monotonicity in surplus sharing," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 23(3), pages 643-658, March.
    19. Leroux, Justin, 2004. "Strategy-proofness and efficiency are incompatible in production economies," Economics Letters, Elsevier, vol. 85(3), pages 335-340, December.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Beviá, Carmen & Corchón, Luis C., 2009. "Cooperative production and efficiency," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 143-154, March.
    2. repec:bla:annpce:v:89:y:2018:i:1:p:87-107 is not listed on IDEAS
    3. Kumar, Rajnish, 2013. "Secure implementation in production economies," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 372-378.
    4. He Liu & Yun Bai & Zhiguang Huang & Han Qiao & Shouyang Wang, 2023. "Private banking development in China under two organizational structures: Economic analysis from an organizational innovation perspective," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-23, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Leroux, Justin, 2005. "Strategyproof Profit Sharing: A Two-Agent Characterization," Working Papers 2005-04, Rice University, Department of Economics.
    2. Leroux, Justin, 2004. "Pooling Private Technologies: Improving upon Autarky," Working Papers 2004-08, Rice University, Department of Economics.
    3. Leroux, Justin, 2005. "Strategyproof Profit Sharing in Partnerships: Improving upon Autarky," Working Papers 2005-05, Rice University, Department of Economics.
    4. Justin Leroux, 2007. "Cooperative production under diminishing marginal returns: interpreting fixed-path methods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(1), pages 35-53, July.
    5. Kumar, Rajnish, 2013. "Secure implementation in production economies," Mathematical Social Sciences, Elsevier, vol. 66(3), pages 372-378.
    6. Beviá, Carmen & Corchón, Luis C., 2009. "Cooperative production and efficiency," Mathematical Social Sciences, Elsevier, vol. 57(2), pages 143-154, March.
    7. Nishizaki, Katsuhiko, 2018. "Secure implementability under Pareto-efficient rules in linear production economies with classical preferences," Research in Economics, Elsevier, vol. 72(3), pages 379-383.
    8. Özgür Kıbrıs & İpek Tapkı, 2014. "A mechanism design approach to allocating central government funds among regional development agencies," Review of Economic Design, Springer;Society for Economic Design, vol. 18(3), pages 163-189, September.
    9. Jens Hougaard & Lars Østerdal, 2009. "Decreasing serial cost sharing: an axiomatic characterization," International Journal of Game Theory, Springer;Game Theory Society, vol. 38(4), pages 469-479, November.
    10. Albizuri, M. Josune & Zarzuelo, Jose M., 2007. "The dual serial cost-sharing rule," Mathematical Social Sciences, Elsevier, vol. 53(2), pages 150-163, March.
    11. Pham, Ngoc Anh, 2019. "Lorenz comparison between Increasing serial and Shapley value cost-sharing rules," Economics Letters, Elsevier, vol. 179(C), pages 49-52.
    12. Kolpin, Van & Wilbur, Dameon, 2005. "Bayesian serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 49(2), pages 201-220, March.
    13. Eric Bahel, 2011. "The implications of the ranking axiom for discrete cost sharing methods," International Journal of Game Theory, Springer;Game Theory Society, vol. 40(3), pages 551-589, August.
    14. M. Albizuri, 2010. "The self-dual serial cost-sharing rule," Theory and Decision, Springer, vol. 69(4), pages 555-567, October.
    15. Hougaard, Jens Leth & Thorlund-Petersen, Lars, 2001. "Mixed serial cost sharing," Mathematical Social Sciences, Elsevier, vol. 41(1), pages 51-68, January.
    16. Hervé Moulin & Yves Sprumont, 2007. "Fair allocation of production externalities : recent results," Revue d'économie politique, Dalloz, vol. 117(1), pages 7-36.
    17. Moulin, Herve & Sprumont, Yves, 2006. "Responsibility and cross-subsidization in cost sharing," Games and Economic Behavior, Elsevier, vol. 55(1), pages 152-188, April.
    18. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2016. "Group Strategy-Proofness in Private Good Economies," American Economic Review, American Economic Association, vol. 106(4), pages 1073-1099, April.
    19. Zare, Marjan & Esmaeili, Maryam & He, Yuanjie, 2019. "Implications of risk-sharing strategies on supply chains with multiple retailers and under random yield," International Journal of Production Economics, Elsevier, vol. 216(C), pages 413-424.
    20. Aadland, David & Kolpin, Van, 2004. "Erratum to "Environmental determinants of cost sharing"," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 105-121, September.

    More about this item

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D23 - Microeconomics - - Production and Organizations - - - Organizational Behavior; Transaction Costs; Property Rights
    • D62 - Microeconomics - - Welfare Economics - - - Externalities

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:gamebe:v:62:y:2008:i:2:p:558-572. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/622836 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.