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Intra Firm Bargaining and Shapley Values

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  • Brügemann, Björn

    () (Vrije Universiteit Amsterdam)

  • Gautier, Pieter A.

    () (Vrije Universiteit Amsterdam)

  • Menzio, Guido

    () (New York University)

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

  • Brügemann, Björn & Gautier, Pieter A. & Menzio, Guido, 2015. "Intra Firm Bargaining and Shapley Values," IZA Discussion Papers 9293, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp9293
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    References listed on IDEAS

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    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.
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    4. Muthoo,Abhinay, 1999. "Bargaining Theory with Applications," Cambridge Books, Cambridge University Press, number 9780521576475, July - De.
    5. 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.
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    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.
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    11. 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.
    12. Gul, Faruk, 1989. "Bargaining Foundations of Shapley Value," Econometrica, Econometric Society, vol. 57(1), pages 81-95, January.
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    Citations

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    Cited by:

    1. Russell Cooper, 2017. "The Employment and Output Effects of Short-Time Work in Germany," 2017 Meeting Papers 613, Society for Economic Dynamics.
    2. Cahuc, Pierre & Carcillo, Stéphane & Le Barbanchon, Thomas, 2017. "The Effectiveness of Hiring Credits," IZA Discussion Papers 11248, Institute of Labor Economics (IZA).
    3. Michele Battisti & Ryan Michaels & Choonsung Park, 2016. "Labor supply within the firm," ifo Working Paper Series 222, ifo Institute - Leibniz Institute for Economic Research at the University of Munich.
    4. Faccini, Renato & Yashiv, Eran, 2017. "The importance of hiring frictions in business cycles," LSE Research Online Documents on Economics 87171, London School of Economics and Political Science, LSE Library.
    5. Victor Aguiar & Roland Pongou & Jean-Baptiste Tondji, 2016. "Measuring and Decomposing the Distance to the Shapley Wage Function with Limited Data," Working Papers 1613e, University of Ottawa, Department of Economics.
    6. Guillaume Rocheteau & Lucie Lebeau & Tai-Wei Hu & Younghwan In, 2018. "Gradual Bargaining in Decentralized Asset Markets," Working Papers 181904, University of California-Irvine, Department of Economics.
    7. Guerrieri, Veronica & Julien, Benoit & Kircher, Philipp & Wright, Randall, 2017. "Directed Search: A Guided Tour," CEPR Discussion Papers 12315, C.E.P.R. Discussion Papers.
    8. repec:wly:iecrev:v:58:y:2017:i::p:889-922 is not listed on IDEAS
    9. Dobbelaere, Sabien & Luttens, Roland Iwan, 2016. "Gradual collective wage bargaining," Labour Economics, Elsevier, vol. 40(C), pages 37-42.
    10. Nicolas Roys, 2016. "Persistence of Shocks and the Reallocation of Labor," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 22, pages 109-130, October.
    11. Ryan Michaels & David Ratner & Michael Elsby, 2016. "Vacancy Chains," 2016 Meeting Papers 753, Society for Economic Dynamics.
    12. Victor Aguiar & Roland Pongou & Jean-Baptiste Tondji, 2017. "A Non-Parametric Approach to Testing the Axioms of the Shapely Value with Limited Data," UWO Department of Economics Working Papers 20172, University of Western Ontario, Department of Economics.
    13. Axel Gottfries, 2018. "Partial commitment in models of on-the-job search with an application to minimum wage spillovers," 2018 Meeting Papers 567, Society for Economic Dynamics.
    14. Hartmut Egger & Simone Habermeyer, 2019. "Nonhomothetic preferences and rent sharing in an open economy," CESifo Working Paper Series 7522, CESifo Group Munich.
    15. repec:oup:revfin:v:23:y:2019:i:2:p:279-323. is not listed on IDEAS

    More about this item

    Keywords

    intra firm bargaining; Shapley value;

    JEL classification:

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

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