Risk aversion and optimal reserve prices in first- and second-price auctions

This paper analyzes the e¤ects of buyer and seller risk aversion in …rst and secondprice auctions. The setting is the classic one of symmetric and independent private values, with ex ante homogeneous bidders. However, the seller is able to optimally set the reserve price. In both auctions the seller’s optimal reserve price is shown to decrease in his own risk aversion, and more so in the …rst-price auction. Thus, greater seller risk aversion increases the ex post e¢ ciency of both auctions, and especially that of the …rst-price auction. The seller’s optimal reserve price in the …rst-price, but not in the second-price, auction decreases in the buyers’risk aversion. Thus, greater buyer risk aversion also increases the ex post e¢ ciency of the …rst but not the second-price auction. At the interim stage, the …rst-price auction is preferred by all buyer types in a lower interval, as well as by the seller. Keywords: …rst-price auction, second-price auction, risk aversion, reserve price JEL classi…cation: D44