Dynamic Mechanism Design: Incentive Compatibility, Prot Maximization and Information Disclosure

We examine the design of incentive-compatible screening mechanisms for dynamic environments in which the agents’types follow a (possibly non-Markov) stochastic process, decisions may be made over time and may a¤ect the type process, and payo¤s need not be time-separable. We derive a formula for the derivative of an agent’s equilibrium payo¤ with respect to his current type in an incentive-compatible mechanism, which summarizes all …rst-order conditions for incentive compatibility and generalizes Mirrlees’s envelope formula of static mechanism design. We provide conditions on the environment under which this formula must hold in any incentivecompatible mechanism. When specialized to quasi-linear environments, this formula yields a dynamic “revenue-equivalence” result and an expression for dynamic virtual surplus, which is instrumental for the design of optimal mechanisms. We also provide some su¢ cient conditions for incentive compatibility, and for its robustness to an agent’s observation of the other agents’ past and future types. We apply these results to a number of novel settings, including the design of pro…t-maximizing auctions and durable-good selling mechanisms for buyers whose values follow an AR(k) process. JEL Classi…cation Numbers: D82, C73, L1. Keywords: asymmetric information, stochastic processes, incentives For useful suggestions, we thank seminar participants at various institutions where this paper was presented. A special thank is to Li Hao and Narayana Kocherlakota for very detailed comments. Pavan also thanks the hospitality of Collegio Carlo Alberto where part of this work was completed. This paper supersedes 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. Earlier versions contained a section on the independentshock approach which has now been incorporated in a companion paper (still work in progress). While waiting for a draft, the reader interested in this part can look at Section 3.3 in the November 2008 version posted on our webpages.