Auction design without quasilinear preferences

Abstract

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 indivisible good for sale is a normal good. I show that removing quasilinearity leads to qualitatively different solutions to the auction design problem. Expected revenue is no longer maximized using standard auctions that allocate the good to the highest bidder. Instead, the auctioneer better exploits bidder preferences by using 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 divisible good in net supply 1. With enough bidders, it has greater expected revenues than any standard auction, and under complete information, it implements a Pareto efficient allocation.

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