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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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    2. Shenzhe Jiang & Junjie Xia & Jiajun Xu & Jianye Yan, 2023. "A theory of National Development Bank: long-term investment and the agency problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(3), pages 995-1024, October.
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