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Optimal Delegation with Multi-dimensional Decisions

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  • Frédéric Koessler

    (PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • David Martimort

    (PSE - Paris-Jourdan Sciences Economiques - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - INRA - Institut National de la Recherche Agronomique - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - ENPC - École des Ponts ParisTech - ENS Paris - École normale supérieure - Paris - PSL - Université Paris sciences et lettres - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique - EHESS - École des hautes études en sciences sociales - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

This paper investigates optimal mechanisms in a principal-agent framework with a two-dimensional decision space, quadratic payoffs and no monetary transfers. If the conflicts of interest between the principal and the agent are different on each dimension, then delegation is always strictly valuable. The principal can better extract information from the agent by using the spread between the two decisions as a costly screening device. Delegation sets no longer trade off pooling intervals and intervals of full discretion but instead take more complex shapes. We use advanced results from the calculus of variations to ensure existence of a solution and derive sufficient and necessary conditions for optimality. The optimal mechanism is continuous and deterministic. The agent's informational rent, the average decision and its spread are strictly monotonic in the agent's type. The comparison of the optimal mechanism with standard one-dimensional mechanisms shows how cooperation between different principals controlling various dimensions of the agent's activities facilitates information revelation.

Suggested Citation

  • Frédéric Koessler & David Martimort, 2012. "Optimal Delegation with Multi-dimensional Decisions," PSE - Labex "OSE-Ouvrir la Science Economique" halshs-00754576, HAL.
  • Handle: RePEc:hal:pseose:halshs-00754576
    DOI: 10.1016/j.jet.2012.05.019
    Note: View the original document on HAL open archive server: https://hal-pjse.archives-ouvertes.fr/halshs-00754576
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Alexander Frankel, 2014. "Aligned Delegation," American Economic Review, American Economic Association, vol. 104(1), pages 66-83, January.
    2. Ambrus, Attila & Egorov, Georgy, 2017. "Delegation and nonmonetary incentives," Journal of Economic Theory, Elsevier, vol. 171(C), pages 101-135.
    3. Tymofiy Mylovanov & Andriy Zapechelnyuk, 2010. "Decision Rules for Experts with Opposing Interests," Working Papers 674, Queen Mary University of London, School of Economics and Finance.
    4. Zapechelnyuk, Andriy, 2013. "Eliciting information from a committee," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2049-2067.
    5. Amador, Manuel & Bagwell, Kyle, 2020. "Money burning in the theory of delegation," Games and Economic Behavior, Elsevier, vol. 121(C), pages 382-412.
    6. Sarah Auster & Nicola Pavoni, 2020. "Limited Awareness and Financial Intermediation," ECONtribute Discussion Papers Series 043, University of Bonn and University of Cologne, Germany.
    7. Tapas Kundu & Tore Nilssen, 2020. "Delegation of Regulation," Journal of Industrial Economics, Wiley Blackwell, vol. 68(3), pages 445-482, September.
    8. Didier Laussel & Ngo Van Long, 2020. "Tying the politicians’ hands: The optimal limits to representative democracy," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(1), pages 25-48, February.
    9. Ricardo Alonso & Isabelle Brocas & Juan D. Carrillo, 2014. "Resource Allocation in the Brain," Review of Economic Studies, Oxford University Press, vol. 81(2), pages 501-534.
    10. Vincent Anesi & Daniel J. Seidmann, 2009. "Optimal Delegation with a Finite Number of States," Discussion Papers 2009-20, The Centre for Decision Research and Experimental Economics, School of Economics, University of Nottingham.
    11. Krähmer, Daniel & Kováč, Eugen, 2016. "Optimal sequential delegation," Journal of Economic Theory, Elsevier, vol. 163(C), pages 849-888.
    12. Sarah Auster & Nicola Pavoni, 2021. "Optimal Delegation and Information Transmission Under Limited Awareness," CRC TR 224 Discussion Paper Series crctr224_2021_256v2, University of Bonn and University of Mannheim, Germany.
    13. Mylovanov, Tymofiy & Zapechelnyuk, Andriy, 2013. "Decision rules revealing commonly known events," Economics Letters, Elsevier, vol. 119(1), pages 8-10.
    14. Murali Agastya & Parimal Kanti Bag & Indranil Chakraborty, 2014. "Communication and authority with a partially informed expert," RAND Journal of Economics, RAND Corporation, vol. 45(1), pages 176-197, March.
    15. Mühlbauer, Stefan, 2016. "Foundation owned firms - a delegation approach," VfS Annual Conference 2016 (Augsburg): Demographic Change 145719, Verein für Socialpolitik / German Economic Association.
    16. Alex Frankel, 2016. "Delegating Multiple Decisions," American Economic Journal: Microeconomics, American Economic Association, vol. 8(4), pages 16-53, November.

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    More about this item

    Keywords

    Mechanism design; Multi-dimensional decision; Delegation; Mechanism;
    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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