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Optimal Dynamic Contracts for a Large-Scale Principal-Agent Hierarchy: A Concavity-Preserving Approach

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  • Christopher W. Miller
  • Insoon Yang

Abstract

We present a continuous-time contract whereby a top-level player can incentivize a hierarchy of players below him to act in his best interest despite only observing the output of his direct subordinate. This paper extends Sannikov's approach from a situation of asymmetric information between a principal and an agent to one of hierarchical information between several players. We develop an iterative algorithm for constructing an incentive compatible contract and define the correct notion of concavity which must be preserved during iteration. We identify conditions under which a dynamic programming construction of an optimal dynamic contract can be reduced to only a one-dimensional state space and one-dimensional control set, independent of the size of the hierarchy. In this sense, our results contribute to the applicability of dynamic programming on dynamic contracts for a large-scale principal-agent hierarchy.

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  • Christopher W. Miller & Insoon Yang, 2015. "Optimal Dynamic Contracts for a Large-Scale Principal-Agent Hierarchy: A Concavity-Preserving Approach," Papers 1506.05497, arXiv.org.
    • Handle: RePEc:arx:papers:1506.05497
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    References listed on IDEAS

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    1. Yuliy Sannikov, 2008. "A Continuous-Time Version of the Principal-Agent Problem," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 75(3), pages 957-984.
    2. Holmstrom, Bengt & Milgrom, Paul, 1987. "Aggregation and Linearity in the Provision of Intertemporal Incentives," Econometrica, Econometric Society, vol. 55(2), pages 303-328, March.
    3. McAfee, R Preston & McMillan, John, 1995. "Organizational Diseconomies of Scale," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 4(3), pages 399-426, Fall.
    4. Yingyi Qian, 1994. "Incentives and Loss of Control in an Optimal Hierarchy," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 61(3), pages 527-544.
    5. Ngo Long & Gerhard Sorger, 2010. "A dynamic principal-agent problem as a feedback Stackelberg differential game," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 18(4), pages 491-509, December.
    6. Weber, Thomas A., 2011. "Optimal Control Theory with Applications in Economics," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262015730, December.
    7. Nahum D. Melumad & Dilip Mookherjee & Stefan Reichelstein, 1995. "Hierarchical Decentralization of Incentive Contracts," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 654-672, Winter.
    8. Hui Ou-Yang, 2003. "Optimal Contracts in a Continuous-Time Delegated Portfolio Management Problem," The Review of Financial Studies, Society for Financial Studies, vol. 16(1), pages 173-208.
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    Cited by:

    1. Thibaut Mastrolia & Dylan Possamai, 2015. "Moral hazard under ambiguity," Papers 1511.03616, arXiv.org, revised Oct 2016.
    2. Emma Hubert, 2023. "Continuous-time incentives in hierarchies," Finance and Stochastics, Springer, vol. 27(3), pages 605-661, July.

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