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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.

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Bibliographic Info

Paper provided by EconWPA in its series Microeconomics with number 9503001.

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Date of creation: 24 Mar 1995
Date of revision: 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. 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.

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