IDEAS home Printed from https://ideas.repec.org/a/wly/emetrp/v83y2015ip729-769.html
   My bibliography  Save this article

A Polynomial Optimization Approach to Principal–Agent Problems

Author

Listed:
  • Philipp Renner
  • Karl Schmedders

Abstract

This paper presents a new method for the analysis of moral hazard principal–agent problems. The new approach avoids the stringent assumptions on the distribution of outcomes made by the classical first‐order approach and instead only requires the agent's expected utility to be a rational function of the action. This assumption allows for a reformulation of the agent's utility maximization problem as an equivalent system of equations and inequalities. This reformulation in turn transforms the principal's utility maximization problem into a nonlinear program. Under the additional assumptions that the principal's expected utility is a polynomial and the agent's expected utility is rational in the wage, the final nonlinear program can be solved to global optimality. The paper also shows how to first approximate expected utility functions that are not rational by polynomials, so that the polynomial optimization approach can be applied to compute an approximate solution to nonpolynomial problems. Finally, the paper demonstrates that the polynomial optimization approach extends to principal–agent models with multidimensional action sets.

Suggested Citation

  • Philipp Renner & Karl Schmedders, 2015. "A Polynomial Optimization Approach to Principal–Agent Problems," Econometrica, Econometric Society, vol. 83, pages 729-769, March.
  • Handle: RePEc:wly:emetrp:v:83:y:2015:i::p:729-769
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/
    Download Restriction: no
    ---><---

    Other versions of this item:

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Philipp Renner & Karl Schmedders, 2020. "Discrete‐time dynamic principal–agent models: Contraction mapping theorem and computational treatment," Quantitative Economics, Econometric Society, vol. 11(4), pages 1215-1251, November.
    2. Singham, D.I., 2019. "Sample average approximation for the continuous type principal-agent problem," European Journal of Operational Research, Elsevier, vol. 275(3), pages 1050-1057.
    3. Philipp Renner & Karl Schmedders, 2017. "Dynamic Principal–Agent Models," Working Papers 203620456, Lancaster University Management School, Economics Department.
    4. Ewerhart, Christian, 2016. "An envelope approach to tournament design," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 1-9.
    5. Chang Koo Chi & Kyoung Jin Choi, 2022. "A Dual Approach To Agency Problems: Existence," Working papers 2022rwp-197, Yonsei University, Yonsei Economics Research Institute.
    6. Bo Chen & Yu Chen & David Rietzke, 2020. "Simple contracts under observable and hidden actions," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(4), pages 1023-1047, June.
    7. Rehbeck, John, 2018. "Note on unique Nash equilibrium in continuous games," Games and Economic Behavior, Elsevier, vol. 110(C), pages 216-225.
    8. Chi, Chang Koo & Choi, Kyoung Jin, 2023. "A dual approach to agency problems," Journal of Mathematical Economics, Elsevier, vol. 109(C).
    9. Kirkegaard, René, 2017. "Moral hazard and the spanning condition without the first-order approach," Games and Economic Behavior, Elsevier, vol. 102(C), pages 373-387.
    10. Philipp Renner, 2020. "An augmented first-order approach for incentive problems," Working Papers 297498586, Lancaster University Management School, Economics Department.
    11. Daniel Krv{s}ek & Dylan Possamai, 2023. "Randomisation with moral hazard: a path to existence of optimal contracts," Papers 2311.13278, arXiv.org.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:emetrp:v:83:y:2015:i::p:729-769. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/essssea.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.