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

Marshall School of Business, University of Southern California, Los Angeles, California 90089
Graduate School of Business, Stanford University, Stanford, California 94305
zhanghao{at}marshall.usc.edu
stefzen{at}stanford.edu

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.

Subject classifications: games; stochastic; dynamic principal-agent model; adverse selection; dynamic programming; Markov; decision processes.
History: Received August 2004; revision received February 2007; accepted February 2007.