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Finite-State Contract Theory with a Principal and a Field of Agents

Author

Listed:
  • René Carmona

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

  • Peiqi Wang

    (Department of Operations Research and Financial Engineering, Princeton University, Princeton, New Jersey 08544)

Abstract

We use the recently developed probabilistic analysis of mean field games with finitely many states in the weak formulation to set up a principal/agent contract theory model where the principal faces a large population of agents interacting in a mean field manner. We reduce the problem to the optimal control of dynamics of the McKean-Vlasov type, and we solve this problem explicitly for a class of models with concave rewards. The paper concludes with a numerical example demonstrating the power of the results when applied to an example of epidemic containment.

Suggested Citation

  • René Carmona & Peiqi Wang, 2021. "Finite-State Contract Theory with a Principal and a Field of Agents," Management Science, INFORMS, vol. 67(8), pages 4725-4741, August.
    • Handle: RePEc:inm:ormnsc:v:67:y:2021:i:8:p:4725-4741
    DOI: 10.1287/mnsc.2020.3760
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    References listed on IDEAS

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    1. Martin F. Hellwig & Klaus M. Schmidt, 2002. "Discrete-Time Approximations of the Holmstrom-Milgrom Brownian-Motion Model of Intertemporal Incentive Provision," Econometrica, Econometric Society, vol. 70(6), pages 2225-2264, November.
    2. 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.
    3. Holmstrom, Bengt & Milgrom, Paul, 1991. "Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design," The Journal of Law, Economics, and Organization, Oxford University Press, vol. 7(0), pages 24-52, Special I.
    4. Samuel N. Cohen & Robert J. Elliott, 2008. "Comparisons for backward stochastic differential equations on Markov chains and related no-arbitrage conditions," Papers 0810.0055, arXiv.org, revised Jan 2010.
    5. Jaeyoung Sung, 1995. "Linearity with Project Selection and Controllable Diffusion Rate in Continuous-Time Principal-Agent Problems," RAND Journal of Economics, The RAND Corporation, vol. 26(4), pages 720-743, Winter.
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