Essays on auctions and mechanism design

In Chapter 1, we consider an auction setting where the buyers are risk averse with private but possibly correlated valuations and characterize the optimal efficient mechanism for a risk neutral seller. In our model the optimal auction extracts all consumer surplus whenever the correlation is stronger than 1/3. We also discuss the case of a risk averse seller facing risk neutral buyers. Under independent private values we show that within each expected revenue equivalence class there is an auction with deterministic revenue for the seller (this is a result joint with Gabor Futo). If the bidders' valuations are correlated then a sufficiently risk averse seller prefers the English auction to any of the full-rent-extracting (Cremer-McLean-) auctions.; In Chapter 2 (a joint paper with Lucy White), we consider a first-price auction where risk-averse bidders bid for an object whose value is risky, and analyze the comparative statics of risk on bidding behavior. In the private values model we show that as risk increases, decreasingly risk-averse bidders reduce their bids by more than the risk premium (we term the effect "precautionary bidding"). Ceteris paribus, bidders will be better off bidding for a more risky object. Even in the presence of this effect, the expected revenue of a first price auction remains higher than that of a second price auction. We also show how this result extends to common values, and suggest empirical tests of the model.; In Chapter 3 we show that Ausubel's generalization of the English auction is efficient for two bidders in a general multi-object setting with common values, but it is generally inefficient for more than two bidders. We propose solutions to this problem: a simple mechanism (parallel English auctions played by all pairs of buyers) in the case of unit demands, and a more complicated one (parallel pairwise Ausubel auctions with an initial round of signal-revelation) when buyers may want several units.; In Chapter 4 (a joint paper with Eric Maskin), we show that when multiple goods are sold, an extension of the Groves-Clarke mechanism (allowing buyers to make their bids contingent on other buyers' valuations) is efficient in a broad class of cases in which buyers have multi-dimensional information and there are common (i.e., interdependent) values.