Dynamic Mechanism Design

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 make public (contractible) and private decisions based on the reports. The probability distribution over future signals may depend on both past signals and past decisions. 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 in each period, so that the mechanism can be made self-enforcing if the horizon is infinite and players are sufficiently patient. Then, assuming Independent Types and continuous signal spaces, I derive a revenue equivalence result showing that any two dynamic mechanisms that implement the same allocation rule must yield the same expected payoffs to the agents and hence the same expected revenue to an auctioneer regardless of the transfer scheme and of the information disclosed by the mechanism to the agents. Using this result, I express the expected profits of an auctioneer as the expectation of “dynamic virtual surplus,” and characterize profit-maximizing mechanisms. As an application, I derive a profit-maximizing sequence of auctions when the bidders’ types follow autoregressive process.

Based on joint papers with Susan Athey and Juuso Toikka
http://www.stanford.edu/~isegal/agv.pdf
http://www.stanford.edu/~isegal/req.pdf