Dynamic Mechanism Design∗

We study the design of incentive-compatible mechanisms in general dynamic environments where information arrives gradually over time and decisions are made over multiple periods. Our first main result is a necessary condition for incentive compatibility that takes the form of an envelope formula for the derivative of an agent’s equilibrium expected payoff with respect to his current type. It combines the familiar marginal effects of types on payoffs with novel marginal effects of current types on future ones captured by the “impulse response functions.”The envelope formula yields an expression for dynamic virtual surplus which is instrumental to the design of optimal mechanisms and to the study of the dynamics of distortions under such mechanisms. We construct transfers that guarantee that the formula is satisfied at all histories and qualify in what sense they are pinned down by the allocation rule (“revenue equivalence”). Our second main result is a characterization of PBE-implementable allocation rules in Markov environments, which yields suffi cient conditions that are applicable also to some non-Markov environments. We illustrate the results by applying them to the design of novel mechanisms for the sale of experience goods (“bandit auctions”). JEL Classification Numbers: D82, C73, L1.