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A Dual Approach To Agency Problems: Existence

Author

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  • Chang Koo Chi

    (Yonsei Univ)

  • Kyoung Jin Choi

    (University of Calgary Haskayne School of Business)

Abstract

This paper presents a dual approach to the standard agency model. We formulate the dual problem corresponding to the principal-agent problem under the assumption that the firstorder approach (FOA) is valid. This dual formulation generates a convex conjugate of a distinctive form, which transforms the agent’s utility from compensation into a dual functional. The dual problem features a simple convex structure, which enables us to perform a comprehensive analysis for the primal problem. We derive novel and more tractable conditions for existence and uniqueness of an optimal FOA contract in terms of the functional. Furthermore, the dual approach provides us with illuminating insights into the previous nonexistence results.

Suggested Citation

  • Chang Koo Chi & Kyoung Jin Choi, 2022. "A Dual Approach To Agency Problems: Existence," Working papers 2022rwp-197, Yonsei University, Yonsei Economics Research Institute.
    • Handle: RePEc:yon:wpaper:2022rwp-197
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    References listed on IDEAS

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    1. Rogerson, William P, 1985. "The First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 53(6), pages 1357-1367, November.
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    5. Ohad Kadan & Philip J. Reny & Jeroen M. Swinkels, 2017. "Existence of Optimal Mechanisms in Principal‐Agent Problems," Econometrica, Econometric Society, vol. 85, pages 769-823, May.
    6. Jung, Jin Yong & Kim, Son Ku, 2015. "Information space conditions for the first-order approach in agency problems," Journal of Economic Theory, Elsevier, vol. 160(C), pages 243-279.
    7. Jewitt, Ian, 1988. "Justifying the First-Order Approach to Principal-Agent Problems," Econometrica, Econometric Society, vol. 56(5), pages 1177-1190, September.
    8. Kirkegaard, René, 2017. "A unifying approach to incentive compatibility in moral hazard problems," Theoretical Economics, Econometric Society, vol. 12(1), January.
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    10. Jewitt, Ian & Kadan, Ohad & Swinkels, Jeroen M., 2008. "Moral hazard with bounded payments," Journal of Economic Theory, Elsevier, vol. 143(1), pages 59-82, November.
    11. Moroni, Sofia & Swinkels, Jeroen, 2014. "Existence and non-existence in the moral hazard problem," Journal of Economic Theory, Elsevier, vol. 150(C), pages 668-682.
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    Cited by:

    1. Chi, Chang Koo & Choi, Kyoung Jin, 2023. "A dual approach to agency problems," Journal of Mathematical Economics, Elsevier, vol. 109(C).

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    More about this item

    Keywords

    Existence; moral hazard; principal-agent models; Lagrange duality;
    All these keywords.

    JEL classification:

    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design
    • D86 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Economics of Contract Law

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