Dynamic mechanism design: Incentive compatibility, profit 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 affect the type process, and payoffs need not be time-separable. We derive a formula for the derivative of an agent's equilibrium payoff with respect to his current type in an incentive-compatible mechanism, which summarizes all first-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 sufficient 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 profit-maximizing auctions and durable-good selling mechanisms for buyers whose values follow an AR(k) process.