We consider truthful implementation of the socially e¢ cient allocation in an independent private-value environment in which agents receive private information over time. We propose a suitable generalization of the pivot mechanism, based on the marginal contribution of each agent. In the dynamic pivot mechanism, the ex-post incentive and ex-post participation constraints are satis…ed for all agents after all histories. In an environment with diverse preferences it is the unique mechanism satisfying ex-post incentive, ex-post participation and e¢ cient exit conditions. We develop the dynamic pivot mechanism in detail for a repeated auction of a single object in which each bidder learns over time her true valuation of the object. We show that the dynamic pivot mechanism is equivalent to a modi…ed second price auction.

We consider a general mechanism design setting where each agent can acquire (covert) information before participating in the mechanism. The central question is whether a mechanism exists that provides the efficient incentives for information acquisition ex-ante and implements the efficient allocation conditional on the private information ex-post. It is shown that in every private value environment the Vickrey-Clark-Groves mechanism guarantees both ex-ante as well as ex-post efficiency. In contrast, with common values, ex-ante and ex-post efficiency cannot be reconciled in general. Sufficient conditions in terms of sub- and supermodularity are provided when (all) ex-post efficient mechanisms lead to private under- or over-acquisition of information.

We consider the situation where a single consumer buys a stream of goods from different sellers over time. The true value of each seller's product to the buyer is initially unknown. Additional information can be gained only by experimentation. For exogeneously given prices the buyer's problem is a multi-armed bandit problem. The innovation in this paper is to endogenize the cost of experimentation to the consumer by allowing for price competition between the sellers. The role of prices is then to allocate intertemporally the costs and benefits of learning between buyers and sellers. We examine how strategic aspects of the oligopoly model interact with the learning process. All Markov perfect equilibria (MPE) are efficient. We identify an equilibrium which besides its unique robustness properties has a strikingly simple, seemingly myopic pricing rule. Prices below marginal cost emerge naturally to sustain experimentation. Intertemporal exchange of the gains of learning is necessary to support efficient experimentation. We analyze the asymptotic behavior of the equilibria.