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Dynamic Principal-Agent Models

Author

Listed:
  • Philipp Renner

    (Stanford University - The Hoover Institution on War, Revolution and Peace)

  • Karl Schmedders

    (University of Zurich)

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. Therefore, the theorem also provides 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 (NLP). We can then solve these nonlinear problems with a standard NLP solver. 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, 2016. "Dynamic Principal-Agent Models," Swiss Finance Institute Research Paper Series 16-26, Swiss Finance Institute.
    • Handle: RePEc:chf:rpseri:rp1626
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    File URL: http://ssrn.com/abstract=2764140
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    Cited by:

    1. Dutta, Prajit K. & Siconolfi, Paolo, 2019. "Asynchronous games with transfers: Uniqueness and optimality," Journal of Economic Theory, Elsevier, vol. 183(C), pages 46-75.

    More about this item

    Keywords

    Optimal unemployment tax; principal-agent model; repeated moral hazard;
    All these keywords.

    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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