I will consider the design of efficient and profit-maximizing Bayesian incentive-compatible mechanisms for general dynamic environments with private information. In the environment, agents observe a sequence of private signals over a number of periods. In each period, the agents report their private signals and choose public (contractible) and private actions based on the reports. The probability distribution over future signals may depend on both past signals and past decisions. The general framework covers a broad class of long-term contracts and mechanisms including advance purchase contracts, repeated auctions, or life-time taxation mechanisms, allowing for serial correlation of agents' types, investments in agents' value or information, learning-by-doing, and habit formation. First I construct an efficient incentive-compatible mechanism, under the assumption of Private Values (each agent's payoff is determined by his own observations). Then I show that budget can be balanced in each period under the assumption of Independent Types (the distribution of each agent's private signals does not depend on the other agents' private information, except through public decisions). I provide conditions under which participation constraints can be satisfied, and the mechanism can be made self-enforcing, provided that the time horizon is infinite and players are sufficiently patient. Next, assuming Independent Types and continuous signal spaces, I derive a "Revenue Equivalence" result showing that when agents' private signals are drawn from continuous intervals, any two dynamic mechanisms that implement the same allocation rule must yield the same expected payoffs to the agents and the same expected revenue to the auctioneer regardless of the transfers used by the mechanisms and of the information disclosed to the agents in the course of the mechanism. I derive a formula that expresses the auctioneer's present expected profits as the present expected value of a dynamic "virtual surplus," extending Myerson's derivation for static auctions. I characterize allocation rules that maximize present expected virtual surplus, and identify the inefficiencies introduced by the profit-maximizing auctioneer. I also provide sufficient conditions for such allocation rules to be implementable in an incentive-compatible mechanism. As applications, I derive a profit-maximizing sequence of auctions when the bidders' types follow autoregressive process, or when bidders learn about their value by consuming the object. Talk by Ilya Segal, Department of Economics, Stanford University, CA.
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