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A Dynamic Principal-Agent Model with Hidden Information: Sequential Optimality Through Truthful State Revelation


  • Hao Zhang

    () (Marshall School of Business, University of Southern California, Los Angeles, California 90089)

  • Stefanos Zenios

    () (Graduate School of Business, Stanford University, Stanford, California 94305)


This paper proposes a general framework for a large class of multiperiod principal-agent problems. In this framework, a principal has a primary stake in the performance of a system but delegates its control to an agent. The underlying system is a Markov decision process, where the state of the system can only be observed by the agent but the agent's action is observed by both parties. This paper develops a dynamic programming algorithm to derive optimal long-term contracts for the principal. The principal indirectly controls the underlying system by offering the agent a menu of continuation utility vectors along public information paths; the agent's best response, expressed in his choice of continuation utilities, induces truthful state revelation and results in actions that maximize the principal's expected payoff. This problem is meaningful to the operations research community because it can be framed as the problem of optimally designing the reward structure of a Markov decision process with hidden states and has many applications of interest as discussed in this paper.

Suggested Citation

  • Hao Zhang & Stefanos Zenios, 2008. "A Dynamic Principal-Agent Model with Hidden Information: Sequential Optimality Through Truthful State Revelation," Operations Research, INFORMS, vol. 56(3), pages 681-696, June.
  • Handle: RePEc:inm:oropre:v:56:y:2008:i:3:p:681-696
    DOI: 10.1287/opre.1070.0451

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    References listed on IDEAS

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    Cited by:

    1. Fang Liu & Tracy R. Lewis & Jing-Sheng Song & Nataliya Kuribko, 2019. "Long-Term Partnership for Achieving Efficient Capacity Allocation," Operations Research, INFORMS, vol. 67(4), pages 984-1001, July.
    2. Hao Zhang & Mahesh Nagarajan & Greys Sošić, 2010. "Dynamic Supplier Contracts Under Asymmetric Inventory Information," Operations Research, INFORMS, vol. 58(5), pages 1380-1397, October.
    3. Hamid Nazerzadeh & Georgia Perakis, 2016. "Technical Note—Nonlinear Pricing Competition with Private Capacity Information," Operations Research, INFORMS, vol. 64(2), pages 329-340, April.
    4. Saghafian, Soroush, 2018. "Ambiguous partially observable Markov decision processes: Structural results and applications," Journal of Economic Theory, Elsevier, vol. 178(C), pages 1-35.
    5. Soroush Saghafian & Xiuli Chao, 2014. "The impact of operational decisions on the design of salesforce incentives," Naval Research Logistics (NRL), John Wiley & Sons, vol. 61(4), pages 320-340, June.
    6. Ying-Ju Chen, 2011. "Optimal Selling Scheme for Heterogeneous Consumers with Uncertain Valuations," Mathematics of Operations Research, INFORMS, vol. 36(4), pages 695-720, November.
    7. Liao, Chen-Nan & Chen, Ying-Ju, 2019. "Role of exchangeable tickets in the optimal menu design for airline tickets," Omega, Elsevier, vol. 89(C), pages 151-163.
    8. Qi Feng & Guoming Lai & Lauren Xiaoyuan Lu, 2015. "Dynamic Bargaining in a Supply Chain with Asymmetric Demand Information," Management Science, INFORMS, vol. 61(2), pages 301-315, February.
    9. Zsolt Bihary & P'eter Ker'enyi, 2019. "Gig Economy: A Dynamic Principal-Agent Model," Papers 1902.10021,
    10. Hao Zhang & Guangwen Kong & Sampath Rajagopalan, 2018. "Contract Design by Service Providers with Private Effort," Management Science, INFORMS, vol. 64(6), pages 2672-2689, June.
    11. Hao Zhang, 2012. "Solving an Infinite Horizon Adverse Selection Model Through Finite Policy Graphs," Operations Research, INFORMS, vol. 60(4), pages 850-864, August.
    12. Gyorgy Attila, 2012. "Agency Problems In Public Sector," Annals of Faculty of Economics, University of Oradea, Faculty of Economics, vol. 1(1), pages 708-712, July.
    13. Wenbo Cai & Ying-Ju Chen, 2017. "Channel management and product design with consumers’ probabilistic choices," International Journal of Production Research, Taylor & Francis Journals, vol. 55(3), pages 904-923, February.
    14. Sechan Oh & Özalp Özer, 2013. "Mechanism Design for Capacity Planning Under Dynamic Evolutions of Asymmetric Demand Forecasts," Management Science, INFORMS, vol. 59(4), pages 987-1007, April.
    15. Yih-Chearng Shiue & Ming-Chang Lee & Pei-Jian Lin & Yao-Wen Huang, 2015. "Investor and venture fund managers remuneration paid mechanism based on principle-agent model," Asian Journal of Empirical Research, Asian Economic and Social Society, vol. 5(9), pages 143-151, September.
    16. Bharadwaj Kadiyala & Özalp Özer & Alain Bensoussan, 2020. "A Mechanism Design Approach to Vendor Managed Inventory," Management Science, INFORMS, vol. 66(6), pages 2628-2652, June.
    17. Hao Zhang, 2012. "Analysis of a Dynamic Adverse Selection Model with Asymptotic Efficiency," Mathematics of Operations Research, INFORMS, vol. 37(3), pages 450-474, August.


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