IDEAS home Printed from https://ideas.repec.org/p/red/sed016/389.html
   My bibliography  Save this paper

Intra Firm Bargaining and Shapley Values

Author

Listed:
  • Pieter Gautier

    (VU University Amsterdam)

  • Guido Menzio

    (University of Pennsylvania)

  • Bjoern Bruegemann

    (VU University Amsterdam)

Abstract

The paper revisits the problem of wage bargaining between a firm and multiple workers. We show that the Subgame Perfect Equilibrium of the extensive-form game proposed by Stole and Zwiebel (1996a) does not imply a profile of wages and profits that coincides with the Shapley values as claimed in their classic paper. We propose an alternative extensive-form bargaining game, the Rolodex Game, that follows a simple and realistic protocol and that, under some mild restrictions, admits a unique Subgame Perfect Equilibrium generating a profile of wages and profits that are equal to the Shapley values. The vast applied literature that refers to the Stole and Zwiebel game to give a game-theoretic foundation to the use of the Shapley values as the outcome of the bargain between a firm and multiple workers should instead refer to the Rolodex game.

Suggested Citation

  • Pieter Gautier & Guido Menzio & Bjoern Bruegemann, 2016. "Intra Firm Bargaining and Shapley Values," 2016 Meeting Papers 389, Society for Economic Dynamics.
  • Handle: RePEc:red:sed016:389
    as

    Download full text from publisher

    File URL: https://red-files-public.s3.amazonaws.com/meetpapers/2016/paper_389.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Nash, John, 1953. "Two-Person Cooperative Games," Econometrica, Econometric Society, vol. 21(1), pages 128-140, April.
    3. Ken Binmore & Ariel Rubinstein & Asher Wolinsky, 1986. "The Nash Bargaining Solution in Economic Modelling," RAND Journal of Economics, The RAND Corporation, vol. 17(2), pages 176-188, Summer.
    4. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475.
    5. repec:hal:spmain:info:hdl:2441/c8dmi8nm4pdjkuc9g8grh35j2 is not listed on IDEAS
    6. Pierre Cahuc & Francois Marque & Etienne Wasmer, 2008. "A Theory Of Wages And Labor Demand With Intra-Firm Bargaining And Matching Frictions," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(3), pages 943-972, August.
    7. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Econometrica, Econometric Society, vol. 70(6), pages 2295-2350, November.
    8. Michael W. L. Elsby & Ryan Michaels, 2013. "Marginal Jobs, Heterogeneous Firms, and Unemployment Flows," American Economic Journal: Macroeconomics, American Economic Association, vol. 5(1), pages 1-48, January.
    9. Elhanan Helpman & Oleg Itskhoki & Stephen Redding, 2010. "Inequality and Unemployment in a Global Economy," Econometrica, Econometric Society, vol. 78(4), pages 1239-1283, July.
    10. Gregory S. Crawford & Ali Yurukoglu, 2012. "The Welfare Effects of Bundling in Multichannel Television Markets," American Economic Review, American Economic Association, vol. 102(2), pages 643-685, April.
    11. I. Sebastian Buhai & Miguel A. Portela & Coen N. Teulings & Aico van Vuuren, 2014. "Returns to Tenure or Seniority?," Econometrica, Econometric Society, vol. 82(2), pages 705-730, March.
    12. Fabien Postel-Vinay & Jean-Marc Robin, 2002. "Equilibrium Wage Dispersion with Worker and Employer Heterogeneity," Post-Print hal-03458567, HAL.
    13. Stole, Lars A & Zwiebel, Jeffrey, 1996. "Organizational Design and Technology Choice under Intrafirm Bargaining," American Economic Review, American Economic Association, vol. 86(1), pages 195-222, March.
    14. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
    15. Lars A. Stole & Jeffrey Zwiebel, 1996. "Intra-firm Bargaining under Non-binding Contracts," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 63(3), pages 375-410.
    16. Catherine C. Fontenay & Joshua S. Gans, 2014. "Bilateral Bargaining with Externalities," Journal of Industrial Economics, Wiley Blackwell, vol. 62(4), pages 756-788, December.
    17. Giuseppe Bertola & Ricardo J. Caballero, 1994. "Cross-Sectional Efficiency and Labour Hoarding in a Matching Model of Unemployment," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(3), pages 435-456.
    18. , & , B., 2014. "Search with multi-worker firms," Theoretical Economics, Econometric Society, vol. 9(3), September.
    19. Shaked, Avner & Sutton, John, 1984. "Involuntary Unemployment as a Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 52(6), pages 1351-1364, November.
    20. repec:hal:spmain:info:hdl:2441/dc0ckec3fcb29ms985085gkbp is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    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. Simon Jäger & Benjamin Schoefer & Samuel Young & Josef Zweimüller, 2020. "Wages and the Value of Nonemployment," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 135(4), pages 1905-1963.
    2. William Hawkins, 2015. "Bargaining with Commitment Between Workers and Large Firms," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 18(2), pages 350-364, April.
    3. Leo Kaas & Philipp Kircher, 2015. "Efficient Firm Dynamics in a Frictional Labor Market," American Economic Review, American Economic Association, vol. 105(10), pages 3030-3060, October.
    4. James S. Costain, 1998. "On the quantitative importance of wage bargaining models," Economics Working Papers 262, Department of Economics and Business, Universitat Pompeu Fabra.
    5. Griem, Fabian & Inderst, Roman, 2020. "Bargaining over Royalties in the Shadow of Litigation," EconStor Preprints 253661, ZBW - Leibniz Information Centre for Economics.
    6. Denant-Boemont, Laurent & Gaigné, Carl & Gaté, Romain, 2018. "Urban spatial structure, transport-related emissions and welfare," Journal of Environmental Economics and Management, Elsevier, vol. 89(C), pages 29-45.
    7. Elhanan Helpman & Oleg Itskhoki & Stephen Redding, 2010. "Inequality and Unemployment in a Global Economy," Econometrica, Econometric Society, vol. 78(4), pages 1239-1283, July.
    8. Binmore, Ken & Osborne, Martin J. & Rubinstein, Ariel, 1992. "Noncooperative models of bargaining," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 7, pages 179-225, Elsevier.
    9. Gabriel Felbermayr & Julien Prat, 2011. "Product Market Regulation, Firm Selection, And Unemployment," Journal of the European Economic Association, European Economic Association, vol. 9(2), pages 278-317, April.
    10. Bauducco, Sofía & Janiak, Alexandre, 2018. "The macroeconomic consequences of raising the minimum wage: Capital accumulation, employment and the wage distribution," European Economic Review, Elsevier, vol. 101(C), pages 57-76.
    11. Shintaro Yamaguchi, 2010. "Job Search, Bargaining, and Wage Dynamics," Journal of Labor Economics, University of Chicago Press, vol. 28(3), pages 595-631, July.
    12. Adachi, Takanori & Tremblay, Mark J., 2020. "Business-to-business bargaining in two-sided markets," European Economic Review, Elsevier, vol. 130(C).
    13. Chakrabarti, Subhadip & Tangsangasaksri, Supanit, 2011. "Labor unions and Nash bargaining using coalition formation games," Mathematical Social Sciences, Elsevier, vol. 62(1), pages 55-64, July.
    14. Shimer, Robert, 2006. "On-the-job search and strategic bargaining," European Economic Review, Elsevier, vol. 50(4), pages 811-830, May.
    15. Alessandro Ruggieri, 2019. "Trade and labour market institutions: A tale of two liberalizations," Discussion Papers 2019-15, University of Nottingham, GEP.
    16. Harold Houba, 2005. "Stochastic Orders of Proposing Players in Bargaining," Tinbergen Institute Discussion Papers 05-063/1, Tinbergen Institute.
    17. Liang Mao, 2017. "Subgame perfect equilibrium in a bargaining model with deterministic procedures," Theory and Decision, Springer, vol. 82(4), pages 485-500, April.
    18. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    19. Mao, Liang, 2015. "Subgame Perfect Equilibrium in a Bargaining Model with Deterministic Procedures," MPRA Paper 67859, University Library of Munich, Germany.
    20. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.

    More about this item

    JEL classification:

    • D21 - Microeconomics - - Production and Organizations - - - Firm Behavior: Theory
    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:red:sed016:389. 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: Christian Zimmermann (email available below). General contact details of provider: https://edirc.repec.org/data/sedddea.html .

    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.