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Optimal delegation with multi-dimensional decisions

Author

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  • Koessler, Frédéric
  • Martimort, David

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 agentʼs informational rent, the average decision and its spread are strictly monotonic in the agentʼs type. The comparison of the optimal mechanism with standard one-dimensional mechanisms shows how cooperation between different principals controlling various dimensions of the agentʼs activities facilitates information revelation.

Suggested Citation

  • Koessler, Frédéric & Martimort, David, 2012. "Optimal delegation with multi-dimensional decisions," Journal of Economic Theory, Elsevier, vol. 147(5), pages 1850-1881.
  • Handle: RePEc:eee:jetheo:v:147:y:2012:i:5:p:1850-1881
    DOI: 10.1016/j.jet.2012.05.019
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    Cited by:

    1. repec:eee:jetheo:v:171:y:2017:i:c:p:101-135 is not listed on IDEAS
    2. 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.
    3. Zapechelnyuk, Andriy, 2013. "Eliciting information from a committee," Journal of Economic Theory, Elsevier, vol. 148(5), pages 2049-2067.
    4. Krähmer, Daniel & Kováč, Eugen, 2016. "Optimal sequential delegation," Journal of Economic Theory, Elsevier, vol. 163(C), pages 849-888.
    5. 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.
    6. 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.
    7. Mylovanov, Tymofiy & Zapechelnyuk, Andriy, 2013. "Decision rules revealing commonly known events," Economics Letters, Elsevier, vol. 119(1), pages 8-10.
    8. 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.
    9. Didier Laussel, 2018. "Tying the Politicians' Hands: The Optimal Limits to Representative Democracy," Working Papers halshs-01690177, HAL.
    10. Mühlbauer, Stefan, 2016. "Foundation owned firms - a delegation approach," Annual Conference 2016 (Augsburg): Demographic Change 145719, Verein für Socialpolitik / German Economic Association.

    More about this item

    Keywords

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

    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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