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

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 payo¤ formula that describes the evolution of the agents’equilibrium payo¤s in an incentive-compatible mechanism. The formula summarizes all local …rst-order conditions taking into account how current information a¤ects 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. First, we 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 show how it permits one to establish a dynamic “revenue-equivalence”result and to construct a formula for dynamic virtual surplus which is instrumental for the design of optimal mechanisms. We then turn to the characterization of su¢ cient conditions for incentive compatibility. Lastly, we show how our results can be put to work in a variety of applications that include the design of pro…t-maximizing dynamic auctions with AR(k) values and the provision of experience goods. JEL numbers: D82, C73, L1. Keywords: dynamic mechanisms, asymmetric information, stochastic processes, incentives 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. For comments and useful suggestions, we thank seminar participants at various conferences and institutions where this paper has been presented. A special thank is to Narayana Kocherlakota for very detailed comments. Pavan also thanks the hospitality of Collegio Carlo Alberto where part of this work was completed. Copyright 2008 by Alessandro Pavan, Ilya Segal, and Juuso Toikka. Any opinions expressed here are those of the authors and not those of Collegio Carlo Alberto.