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Optimal Delegation with Multi-dimensional Decisions

Author

Listed:
  • Frédéric Koessler

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

  • David Martimort

    (PSE - Paris-Jourdan Sciences Economiques - ENS-PSL - 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 nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École nationale des ponts et chaussées - CNRS - Centre National de la Recherche Scientifique - 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," Post-Print halshs-00754576, HAL.
    • Handle: RePEc:hal:journl:halshs-00754576
    DOI: 10.1016/j.jet.2012.05.019
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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. Daniel Habermacher, 2022. "Authority and Specialization under Informational Interdependence," Working Papers 142, Red Nacional de Investigadores en Economía (RedNIE).
    7. 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.
    8. Ricardo Alonso & Isabelle Brocas & Juan D. Carrillo, 2014. "Resource Allocation in the Brain," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 81(2), pages 501-534.
    9. Krähmer, Daniel & Kováč, Eugen, 2016. "Optimal sequential delegation," Journal of Economic Theory, Elsevier, vol. 163(C), pages 849-888.
    10. Alberrto Bennardo & Antonio Abatemarco, 2024. "Multiple tasks, hard information gathering, muted incentives and specialization by project," CELPE Discussion Papers 170, CELPE - CEnter for Labor and Political Economics, University of Salerno, Italy.
    11. Auster, Sarah & Pavoni, Nicola, 2024. "Optimal delegation and information transmission under limited awareness," Theoretical Economics, Econometric Society, vol. 19(1), January.
    12. Andreas Kleiner, 2022. "Optimal Delegation in a Multidimensional World," Papers 2208.11835, arXiv.org.
    13. 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.
    14. Tapas Kundu & Tore Nilssen, 2020. "Delegation of Regulation," Journal of Industrial Economics, Wiley Blackwell, vol. 68(3), pages 445-482, September.
    15. Mylovanov, Tymofiy & Zapechelnyuk, Andriy, 2013. "Decision rules revealing commonly known events," Economics Letters, Elsevier, vol. 119(1), pages 8-10.
    16. 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.
    17. Patrick Lahr & Axel Niemeyer, 2024. "Extreme Points in Multi-Dimensional Screening," Papers 2412.00649, arXiv.org, revised Oct 2025.
    18. Mühlbauer, Stefan, 2016. "Foundation owned firms - a delegation approach," VfS Annual Conference 2016 (Augsburg): Demographic Change 145719, Verein für Socialpolitik / German Economic Association.
    19. Alex Frankel, 2016. "Delegating Multiple Decisions," American Economic Journal: Microeconomics, American Economic Association, vol. 8(4), pages 16-53, November.
    20. Sarah Auster & Nicola Pavoni, 2020. "Limited Awareness and Financial Intermediation," CRC TR 224 Discussion Paper Series crctr224_2020_252, University of Bonn and University of Mannheim, Germany.

    More about this item

    Keywords

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    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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