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Optimal Contract to Induce Continued Effort

Author

Listed:
  • Peng Sun

    (Fuqua School of Business, Duke University, Durham, North Carolina 27708)

  • Feng Tian

    (University of Michigan, Ann Arbor, Michigan 48109)

Abstract

We consider a basic model of a risk-neutral principal incentivizing a risk-neutral agent to exert effort to raise the arrival rate of a Poisson process. The effort is costly to the agent, is unobservable to the principal, and affects the instantaneous arrival rate. Each arrival yields a constant revenue to the principal. The principal, therefore, devises a mechanism involving payments and a potential stopping time to motivate the agent to always exert effort. We formulate this problem as a stochastic optimal control model with an incentive constraint in continuous time over an infinite horizon. Although we allow payments to take general forms contingent on past arrival times, the optimal contract has a simple and intuitive structure, which depends on whether the agent is as patient as or less patient than the principal toward future income.

Suggested Citation

  • Peng Sun & Feng Tian, 2018. "Optimal Contract to Induce Continued Effort," Management Science, INFORMS, vol. 64(9), pages 4193-4217, September.
    • Handle: RePEc:inm:ormnsc:v:64:y:2018:i:9:p:4193-4217
    DOI: 10.1287/mnsc.2017.2826
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    References listed on IDEAS

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    1. Bruno Biais & Thomas Mariotti & Guillaume Plantin & Jean-Charles Rochet, 2007. "Dynamic Security Design: Convergence to Continuous Time and Asset Pricing Implications," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 74(2), pages 345-390.
    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. Bruno Biais & Thomas Mariotti & Jean-Charles Rochet & StÈphane Villeneuve, 2010. "Large Risks, Limited Liability, and Dynamic Moral Hazard," Econometrica, Econometric Society, vol. 78(1), pages 73-118, January.
    4. Fernandes, Ana & Phelan, Christopher, 2000. "A Recursive Formulation for Repeated Agency with History Dependence," Journal of Economic Theory, Elsevier, vol. 91(2), pages 223-247, April.
    5. Erica L. Plambeck & Stefanos A. Zenios, 2003. "Incentive Efficient Control of a Make-to-Stock Production System," Operations Research, INFORMS, vol. 51(3), pages 371-386, June.
    6. Thomas, Jonathan & Worrall, Tim, 1990. "Income fluctuation and asymmetric information: An example of a repeated principal-agent problem," Journal of Economic Theory, Elsevier, vol. 51(2), pages 367-390, August.
    7. Yaping Shan, 2017. "Optimal contracts for research agents," RAND Journal of Economics, RAND Corporation, vol. 48(1), pages 94-124, March.
    8. Brett Green & Curtis R. Taylor, 2016. "Breakthroughs, Deadlines, and Self-Reported Progress: Contracting for Multistage Projects," American Economic Review, American Economic Association, vol. 106(12), pages 3660-3699, December.
    9. Lars Ljungqvist & Thomas J. Sargent, 2004. "Recursive Macroeconomic Theory, 2nd Edition," MIT Press Books, The MIT Press, edition 2, volume 1, number 026212274x, December.
    10. John Y. Zhu, 2013. "Optimal Contracts with Shirking," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 80(2), pages 812-839.
    11. Stephen E. Spear & Sanjay Srivastava, 1987. "On Repeated Moral Hazard with Discounting," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(4), pages 599-617.
    12. PETER M. DeMARZO & YULIY SANNIKOV, 2006. "Optimal Security Design and Dynamic Capital Structure in a Continuous‐Time Agency Model," Journal of Finance, American Finance Association, vol. 61(6), pages 2681-2724, December.
    13. Robin Mason & Juuso Välimäki, 2015. "Getting It Done: Dynamic Incentives To Complete A Project," Journal of the European Economic Association, European Economic Association, vol. 13(1), pages 62-97, February.
    14. Roger B. Myerson, 2015. "Moral Hazard in High Office and the Dynamics of Aristocracy," Econometrica, Econometric Society, vol. 83, pages 2083-2126, November.
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