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Intra Firm Bargaining and Shapley Values

Author

Listed:
  • Björn Brügemann
  • Pieter Gautier
  • Guido Menzio

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

  • Björn Brügemann & Pieter Gautier & Guido Menzio, 2015. "Intra Firm Bargaining and Shapley Values," NBER Working Papers 21508, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:21508
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    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, October.
    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," Review of Economic Studies, Oxford University Press, 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," Review of Economic Studies, Oxford University Press, 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
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    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

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