• DOI:10.1287/opre.1070.0451
• Corpus ID: 18931625

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

@article{Zhang2008ADP,
  title={A Dynamic Principal-Agent Model with Hidden Information: Sequential Optimality Through Truthful State Revelation},
  author={H. Zhang and Stefanos A. Zenios},
  journal={Oper. Res.},
  year={2008},
  volume={56},
  pages={681-696}
}

• H. Zhang, S. Zenios
• Published 1 May 2008
• Economics
• Oper. Res.

The principal-agent paradigm has been extensively studied in economics and attracted attention in operations research. A dynamic principal-agent model with an underlying Markov decision process (MDP) is especially useful in operations research because MDP is one of the most mature modeling tools in this field. In this model, the principal delegates the control of the system to the agent and the agent has access to private information, either of the state of the system or of the agent's actions. These two cases correspond to the two types of the principal-agent models: the hidden information (adverse selection) models and the hidden action (moral hazard) models. While the literature on the hidden information models is vast, most of the existing results can be viewed as special cases of a more general model. However, the study of the general model is absent from the literature.
This dissertation develops a theory to analyze a general dynamic principal-agent model with hidden information. The state of the system is unobserved by the principal while the actions are both observable and verifiable. The principal's problem is to design a compensation mechanism for the agent that utilizes public verifiable history and that maximizes the principal's objective. It can be shown that there exists an optimal compensation mechanism in which the agent truthfully reports the underlying system state. Furthermore, this mechanism is sequentially efficient: there does not exist another mechanism that offers the agent the same utility as the original mechanism and improves the principal's utility in at least one state in one period. The second result implies that the principal can obtain an optimal mechanism by dynamic programming, based on the agent's expected future utility from each period. The solution of the dynamic programming recursion can be formulated as a sequence of multi-stage optimization problems with constraints that capture the truth-telling requirement.
There are many interesting managerial problems where state variables are private information as in this model. Therefore, the model analyzed in this dissertation is not only of significant theoretical interest but can also shed light on significant real-world problems.