Intervention with Private Information, Imperfect Monitoring and Costly Communication

This paper studies the interaction between a designer and a group of strategic and self-interested users who possess information the designer does not have. Because the users are strategic and self-interested, they will act to their own advantage, which will often be different from the interest of the designer, even if the latter is benevolent and seeks to maximize (some measure of) social welfare. In the settings we consider, the designer and the users can communicate (perhaps with noise), the designer can observe the actions of the users (perhaps with error) and the designer can commit to (plans of) actions - interventions - of its own. The designer's problem is to construct and implement a mechanism that provides incentives for the users to communicate and act in such a way as to further the interest of the designer - despite the fact that they are strategic and self-interested and possess private information. To address the designer's problem we propose a general and flexible framework that applies to many scenarios. To illustrate the usefulness of this framework, we discuss some simple examples, leaving further applications to other papers. In an important class of environments, we find conditions under which the designer can obtain its benchmark optimum - the utility that could be obtained if it had all information and could command the actions of the users - and conditions under which it cannot. More broadly we are able to characterize the solution to the designer's problem, even when it does not yield the benchmark optimum. Because the optimal mechanism may be difficult to construct and implement, we also propose a simpler and more readily implemented mechanism that, while falling short of the optimum, still yields the designer a "good" result.