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Dynamic Principal–Agent Models

Author

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  • Philipp Renner
  • Karl Schmedders

Abstract

This paper contributes to the theoretical and numerical analysis of discrete time dynamic principal-agent problems with continuous choice sets. We first provide a new and simplified proof for the recursive reformulation of the sequential dynamic principal-agent relationship. Next we prove the existence of a unique solution for the principal's value function, which solves the dynamic programming problem in the recursive formulation. By showing that the Bellman operator is a contraction mapping, we also obtain a convergence result for the value function iteration. To compute a solution for the problem, we have to solve a collection of static principal{agent problems at each iteration. Under the assumption that the agent's expected utility is a rational function of his action, we can transform the bi-level optimization problem into a standard nonlinear program. The final results of our solution method are numerical approximations of the policy and value functions for the dynamic principal-agent model. We illustrate our solution method by solving variations of two prominent social planning models from the economics literature.

Suggested Citation

  • Philipp Renner & Karl Schmedders, 2017. "Dynamic Principal–Agent Models," Working Papers 203620456, Lancaster University Management School, Economics Department.
  • Handle: RePEc:lan:wpaper:203620456
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    File URL: http://www.lancaster.ac.uk/media/lancaster-university/content-assets/documents/lums/economics/working-papers/LancasterWP2017_028.pdf
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    References listed on IDEAS

    as
    1. Kenneth L. Judd, 1998. "Numerical Methods in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262100711.
    2. J. A. Mirrlees, 1999. "The Theory of Moral Hazard and Unobservable Behaviour: Part I," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 3-21.
    3. Zhao, Rui R., 2007. "Dynamic risk-sharing with two-sided moral hazard," Journal of Economic Theory, Elsevier, vol. 136(1), pages 601-640, September.
    4. Philipp Renner & Karl Schmedders, 2015. "A Polynomial Optimization Approach to Principal–Agent Problems," Econometrica, Econometric Society, vol. 83, pages 729-769, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Optimal unemployment tax; principal-agent model; repeated moral hazard;

    JEL classification:

    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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