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Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion, Model of Intertemporal Incentive Provision

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Author Info
Hellwig, Martin () (Sonderforschungsbereich 504)
Schmidt, Klaus M. () (Universität München)

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Abstract

This paper studies the relation between multi-period discrete-time and continuous-time principal-agent models. We explicitly derive the continuous-time model as a limit of discrete-time models with ever shorter periods and show that the optimal incentive scheme in the continuous model, which is linear in accounts, can be approximated by a sequence of optimal incentive schemes in the discrete models. For a variant of the discrete-time model in which the principal observes only total profits at the end of the last period and where the agent can destroy profits unnoticed we show, that if the length of each period is sufficiently small, then an incentive scheme that is linear in total profits is approximately optimal.

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Paper provided by Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim in its series Sonderforschungsbereich 504 Publications with number 98-06.

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Length: 58 pages
Date of creation: 07 May 1998
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Handle: RePEc:xrs:sfbmaa:98-06

Note: For helpful comments and discussions we are grateful to Darell Duffie, Oliver Hart, Bengt Holmström, Nobuhiro Kiyotaki, John Moore, Holger Müller, Sven Rady, and Jae Sung. We are also grateful for research support from the Schweizerischer Nationalfonds, the Deutsche Forschungsgemeinschaft, and the Taussig Chair at Harvard University.
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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  1. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November. [Downloadable!] (restricted)
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  2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-28, March. [Downloadable!] (restricted)
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  3. Itoh, Hideshi, 1992. "Cooperation in Hierarchical Organizations: An Incentive Perspective," Journal of Law, Economics and Organization, Oxford University Press, vol. 8(2), pages 321-45, April.
  4. Mirrlees, J A, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," Review of Economic Studies, Blackwell Publishing, vol. 66(1), pages 3-21, January. [Downloadable!] (restricted)
  5. Müller, Holger M., 1997. "Randomization in Dynamic Principal-Agent Problems," Sonderforschungsbereich 504 Publications 97-37, Sonderforschungsbereich 504, Universität Mannheim & Sonderforschungsbereich 504, University of Mannheim. [Downloadable!]
  6. Grossman, Sanford J & Hart, Oliver D, 1983. "An Analysis of the Principal-Agent Problem," Econometrica, Econometric Society, vol. 51(1), pages 7-45, January. [Downloadable!] (restricted)
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  7. Hellwig, Martin F., 1996. "Sequential decisions under uncertainty and the maximum theorem," Journal of Mathematical Economics, Elsevier, vol. 25(4), pages 443-464. [Downloadable!] (restricted)
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Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Ernst Fehr & Klaus M. Schmidt, . "Fairness and Incentives in a Multi-Task Principal-Agent Model," IEW - Working Papers iewwp191, Institute for Empirical Research in Economics - IEW. [Downloadable!]
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  2. Coles, Jeffrey & Lemmon, Michael & Meschke, Felix, 2007. "Structural Models and Endogeneity in Corporate Finance: the Link Between Managerial Ownership and Corporate Performance," MPRA Paper 4374, University Library of Munich, Germany, revised 15 Feb 2007. [Downloadable!]
  3. Drew Fudenberg & David K Levine, 2007. "Continuous Time Limits of Repeated Games with Imperfect Public Monitoring," Levine's Working Paper Archive 699152000000000028, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. Hellwig, Martin F. & Schmidt, Klaus M., 2001. "Discrete-Time Approximations of the Holmström-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Discussion Papers in Economics 22, University of Munich, Department of Economics. [Downloadable!]
    Other versions:
  5. Drew Fudenberg & David K Levine, 2007. "Repeated Games with Frequent Signals," Levine's Working Paper Archive 814577000000000009, UCLA Department of Economics. [Downloadable!]
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