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Continuous Approximations in the Study of Hierarchies

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  • Timothy Van Zandt

    (Princeton University)

Abstract

Large organizations are typically modeled as hierarchies. Hierarchies are discrete structures (trees), but researchers frequently use continuous approximations. The purpose of this paper is to study the validity of these approximations. I show that modeling hierarchies with a continuum of tiers is not a good approximation. I also show, for a particular model of balanced hierarchies, that ignoring rounding operators and integer constraints in formulae derived from the discrete model can be a valid approximation, when hierarchies are suitably large. This is made precise by bounds on the relative errors of the approximations.

Suggested Citation

  • Timothy Van Zandt, 1995. "Continuous Approximations in the Study of Hierarchies," Microeconomics 9503001, University Library of Munich, Germany, revised 16 Dec 1997.
    • Handle: RePEc:wpa:wuwpmi:9503001
    Note: Published in Rand Journal of Economics, 26:575-590, 1995. (Contact author for a hard copy.)
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    Cited by:

    1. Van Zandt, Timothy, 2004. "Balancedness of Real-Time Hierarchical Resource Allocation," CEPR Discussion Papers 4276, C.E.P.R. Discussion Papers.
    2. Phillip J. Lederer & Xiaobo Zheng, 2021. "Can information economics explain the organization of productive facilities?," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 30(3), pages 525-553, August.
    3. Andrea Patacconi, 2009. "Coordination and delay in hierarchies," RAND Journal of Economics, RAND Corporation, vol. 40(1), pages 190-208, March.
    4. Saikat Datta, 1996. "On Control Losses In Hierarchies," Rationality and Society, , vol. 8(4), pages 387-412, November.
    5. Jacek Cukrowski & Manfred M. Fischer, 2007. "Efficient organization of information processing," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 28(1), pages 13-26.
    6. Meagher, Kieron J., 2003. "Generalizing incentives and loss of control in an optimal hierarchy: the role of information technology," Economics Letters, Elsevier, vol. 78(2), pages 273-280, February.
    7. Andrea Patacconi, 2005. "Optimal Coordination in Hierarchies," Economics Series Working Papers 238, University of Oxford, Department of Economics.

    More about this item

    JEL classification:

    • D1 - Microeconomics - - Household Behavior
    • D2 - Microeconomics - - Production and Organizations
    • D3 - Microeconomics - - Distribution
    • D4 - Microeconomics - - Market Structure, Pricing, and Design

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