The standard profit-maximizing multi-unit auction can be represented as the Vickrey-Groves-Clarke mechanism in which the seller manipulates his reservation supply curve. The optimal supply curve depends on the distribution from which the buyers' valuations are drawn. However, when this...

There are two basic approaches to deterring socially harmful behavior: with the threat of litigation by private parties or with enforcement by public agencies. Both approaches are used in most countries, but in varying degrees. Private litigation is common in the United States and (to a lesser...

We study the effects of antitrust policy in industries with continual innovation. A more protective antitrust policy may have conflicting effects on innovation incentives, raising the profits of new entrants, but lowering those of continuing incumbents. We show that the direction of the net...

The standard envelope theorems apply to choice sets with convex and topological structure, providing sufficient conditions for the value function to be differentiable in a parameter and characterizing its derivative. This paper studies optimization with arbitrary choice sets and shows that the...

The paper studies the implementation problem, first analyzed by Maskin and Moore (1999), in which two agents observe an unverifiable state of nature and may renegotiate inefficient outcomes following play of the mechanism. We develop a first-order approach to characterizing the set of...

We study users' response to sponsored-search advertising using data from Microsoft's Live AdCenter distributed in the "Beyond Search" initiative. We estimate a structural model of utility maximizing users, which quantifies "user experience" based on their "revealed preferences," and predicts...

The paper studies inefficiencies arising in contracting between one principal and N agents when each agent's utility depends on all agents' trades with the principal. When the principal commits to publicly observed bilateral contracts, the distortion is due to the externalities on agents'...

We consider Bayesian incentive-compatible mechanisms with independent types and either private values or interdependent values that satisfy a form of "congruence." We show that in these settings, interim participation constraints are satisfied when the status quo is the randomized allocation...

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...

The paper considers the communication complexity (measured in bits or real numbers) of Nash implementation of social choice rules. A key distinction is whether we restrict to the traditional one-stage mechanisms or allow multi-stage mechanisms. For one-stage mechanisms, the paper shows that for...