Auction Design Without Quasilinear Preferences

I analyze private value auction design and assume only that bidders are risk averse and have positive wealth effects (i.e. the good is normal). I show removing the standard quasilinearity restriction leads to qualitatively different solutions to the auction design problem with respect to both efficiency or revenue maximization. On efficiency, I show that probabilistic allocations of the good can Pareto dominate the second price auction; and there is no dominant-strategy mechanism that is both Pareto efficient and individually rationality. On revenue, I construct a probability demand mechanism with greater expected revenues than standard auctions when there are sufficiently many bidders. In addition, I take a new approach to studying bid behavior when types are multidimensional. Instead of characterizing bidder's interim incentive constraints, I place bounds on their bids, and I show that these bounds are sufficient for obtaining revenue comparisons