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Measuring and Decomposing the Distance to the Shapley Wage Function with Limited Data

Author

Listed:
  • Victor Aguiar

    (Department of Economics, University of Western Ontario)

  • Roland Pongou

    (Department of Economics, University of Ottawa)

  • Jean-Baptiste Tondji

    (Department of Economics, University of Ottawa)

Abstract

We study the Shapley wage function, a wage scheme in which a worker's pay depends both on the number of hours worked and on the output of the firm. We then provide a way to measure the distance of an arbitrary wage scheme to this function in limited datasets. In particular, for a fixed technology and a given supply of labor, this distance is additively decomposable into violations of the classical axioms of efficiency, equal treatment of identical workers, and marginality. The findings have testable implications for the different ways in which popular wage schemes violate basic properties of distributive justice in market organizations. Applications to the linear contract and to other well-known compensation schemes are shown.

Suggested Citation

  • 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.
    • Handle: RePEc:ott:wpaper:1613e
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    References listed on IDEAS

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    1. Geoffroy de Clippel & Kareen Rozen, 2022. "Fairness through the Lens of Cooperative Game Theory: An Experimental Approach," American Economic Journal: Microeconomics, American Economic Association, vol. 14(3), pages 810-836, August.
    2. Aguiar, Victor H. & Serrano, Roberto, 2017. "Slutsky matrix norms: The size, classification, and comparative statics of bounded rationality," Journal of Economic Theory, Elsevier, vol. 172(C), pages 163-201.
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    4. Björn Brügemann & Pieter Gautier & Guido Menzio, 2019. "Intra Firm Bargaining and Shapley Values," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(2), pages 564-592.
    5. Roth, Alvin, 2012. "The Shapley Value as a von Neumann-Morgenstern Utility," Ekonomicheskaya Politika / Economic Policy, Russian Presidential Academy of National Economy and Public Administration, vol. 6, pages 1-9.
    6. Geoffroy de Clippel & Roberto Serrano, 2005. "Marginal Contributions and Externalities in the Value," Working Papers 2005-11, Brown University, Department of Economics.
    7. 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.
    8. Geoffroy de Clippel & Roberto Serrano, 2008. "Marginal Contributions and Externalities in the Value," Econometrica, Econometric Society, vol. 76(6), pages 1413-1436, November.
    9. Geoffroy de Clippel & Kareen Rozen, 2020. "Fairness through the Lens of Cooperative Game Theory: An Experimental Approach," Working Papers 2020-09, Brown University, Department of Economics.
    10. Moulin, Herve, 1992. "An Application of the Shapley Value to Fair Division with Money," Econometrica, Econometric Society, vol. 60(6), pages 1331-1349, November.
    11. , & , B., 2014. "Search with multi-worker firms," Theoretical Economics, Econometric Society, vol. 9(3), September.
    12. L. S. Shapley & Martin Shubik, 1967. "Ownership and the Production Function," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 81(1), pages 88-111.
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    Cited by:

    1. Tido Takeng, Rodrigue, 2022. "Uncertain production environment and communication structure," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    2. Pongou, Roland & Tondji, Jean-Baptiste, 2018. "Valuing inputs under supply uncertainty: The Bayesian Shapley value," Games and Economic Behavior, Elsevier, vol. 108(C), pages 206-224.

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    More about this item

    Keywords

    Shapley wage function; firm; fairness violations; linear contract; bargaining; limited data;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D20 - Microeconomics - - Production and Organizations - - - General
    • D30 - Microeconomics - - Distribution - - - General
    • J30 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - General

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