Consider a setting with n sellers having i.i.d. costs with log-concave density f from cumulative F, and a buyer who puts a premium [Delta]i on procuring from seller i. We show how for any given [Delta]1,...,[Delta]n, a simple second price bonus auction can be chosen which comes surprisingly...

We study the moral hazard problem without the first-order approach or other common structure. We present sufficient conditions under which the shadow value of simultaneously tightening the minimum payment and individual rationality constraints has a simple and intuitive expression. We then show...

We provide new tools for studying asymmetric first price auctions, connecting their equilibria to the ρ-concavity of the underlying type distributions, and showing how one can use surplus expressions for symmetric auctions to bound equilibrium behavior in asymmetric auctions. We apply these...

Consider a moral hazard problem in which there is a constraint to pay the agent no less than some amount m. This paper studies the effect of changes in m on the effort that the principal chooses to induce from the agent. We present sufficient conditions on the informativeness of the signal...

The tension between allocative efficiency and information aggregation is explored in the context of an auction: k identical objects of unknown quality are auctioned off to n bidders whose tastes affect their valuation of an object of given quality. Bidders receive a signal about the quality of...

We show existence of equilibria in distributional strategies for a wide class of private value auctions, including the first general existence result for double auctions. The set of equilibria is invariant to the tie-breaking rule. The model incorporates multiple unit demands, all standard...

We consider large double auctions with private values. Values need be neither symmetric nor independent. Multiple units may be owned or desired. Participation may be stochastic. We introduce a very mild notion of "a little independence." We prove that all nontrivial equilibria of auctions that...