Dynamic Mechanism Design: Revenue Equivalence, Prot Maximization and Information Disclosure Preliminary and incomplete

This paper examines the problem of how to design incentive-compatible mechanisms in environments in which the agents’private information evolves stochastically over time and in which decisions have to be made in each period. The environments we consider are fairly general in that the agents’types are allowed to evolve in a non-Markov way, decisions are allowed to a¤ect the type distributions and payo¤s are not restricted to be separable over time. Our …rst result is the characterization of a dynamic formula for (the derivative of) the agents’equilibrium payo¤s in an incentive-compatible mechanism. The formula summarizes all local …rst-order conditions taking into account how current types a¤ect the dynamics of expected payo¤s. The formula generalizes the familiar envelope condition from static mechanism design: the key di¤erence is that a variation in the current types now impacts payo¤s in all subsequent periods both directly and through the e¤ect on the distributions of future types. We …rst identify assumptions on the primitive environment that guarantee that our dynamic payo¤ formula is a necessary condition for incentive compatibility. Next, we specialize this formula to quasi-linear environments and use it to establish a dynamic revenue-equivalence result. Lastly, we turn to the characterization of su¢ cient conditions for incentive compatibility. We then apply the results to study the properties of revenue-maximizing mechanisms in a variety of applications that include dynamic auctions with AR(k) values and the provision of experience goods. JEL Classi…cation Numbers: D82, C73, L1. Keywords: dynamic mechanisms, asymmetric information, stochastic processes, long-term contracting, incentives This paper supercedes previous working papers “Revenue Equivalence, Pro…t Maximization, and Transparency in Dynamic Mechanisms”by Segal and Toikka and “Long-Term Contracting in a Changing World”by Pavan. Acknowledgements to be added.