Auction design without quasilinear preferences

I study the canonical private value auction model for a single good without the quasilinearity restriction. I assume only that bidders are risk averse and the indi- visible good for sale is a normal good. I show that removing quasilinearity leads to qualitatively different solutions to the auction design problem. Expected rev- enue is no longer maximized using standard auctions that allocate the good to the highest bidder. Instead, the auctioneer better exploits bidder preferences by us- ing a mechanism that allocates the good to one of many different bidders, each with strictly positive probability. I introduce a probability demand mechanism that treats probabilities of winning the indivisible good like a d ivisible good in net supply 1. With enough bidders, it has greater expected revenues than any stan- dard auction, and under complete information, it implements a Pareto ef?cient allocation.