Performance-based incentives in a dynamic principal–agent model

The principal–agent paradigm, in which a principal has a primary stake in the performance of some system but delegates operational control of that system to an agent, has many natural applications in operations management (OM). However, existing principal–agent models are of limited use to OM researchers because they cannot represent the rich dynamic structure required of OM models. This paper formulates a novel dynamic model that overcomes these limitations by combining the principal–agent framework with the physical structure of a Markov decision process. In this model one has a system moving from state to state as time passes, with transition probabilities depending on actions chosen by an agent, and a principal who pays the agent based on state transitions observed. The principal seeks an optimal payment scheme, striving to induce the actions that will maximize her expected discounted profits over a finite planning horizon. Although dynamic principal–agent models similar to the one proposed here are considered intractable, a set of assumptions are introduced that enable a systematic analysis. These assumptions involve the economic structure of the model but not its physical structure. Under these assumptions, the paper establishes that one can use a dynamic-programming recursion to derive an optimal payment scheme. This scheme is memoryless and satisfies a generalization of Bellman's principle of optimality. Important managerial insights are highlighted in the context of a two-state example called the maintenance problem.