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

We examine the design of incentive-compatible screening mechanisms for dynamic environ- ments in which the agents'types follow a (possibly non-Markov) stochastic process, decisions may be made over time and may aect the type process, and payos need not be time-separable. We derive a formula for the derivative of an agent's equilibrium payowith respect to his cur- rent 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 incentive- compatible 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 de- sign of pro…t-maximizing auctions and durable-good selling mechanisms for buyers whose values