The Interaction between Decision and Control Problems and the Value of Information

We study a model of double moral hazard in which an information system is used in a decision problem (the principal can choose her own act based on the information) and a control problem (the principal can use the information to motivate the agent). An information system that provides more information is strictly preferred to an information system that provides less information if either of the problems is considered in isolation. However, less information, even though all information is public and contractible, can in fact be desirable from a profit maximization perspective because of an interaction between the two problems. Choosing an information system that provides less information serves as a substitute for commitment for the principal in our model. We also provide sufficient conditions for more information to be preferred, one of which is the complementarity of the agents act and the principal's act in the way they influence a joint measure of performance.