Audrey Hu

Risk Aversion and Optimal Reserve Prices in First and Second-Price Auctions

This paper analyzes the effects of buyer and seller risk aversion in first and second-price 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 first-price auction. Thus, greater seller risk aversion increases the ex post efficiency of both auctions, and especially that of the first-price auction. The seller’s optimal reserve price in the first-price, but not in the second-price, auction decreases in the buyers’ risk aversion. Thus, greater buyer risk aversion also increases the ex post efficiency of the first but not the second-price auction. At the interim stage, the first-price auction is preferred by all buyer types in a lower interval, as well as by the seller.

Premium auctions and risk preferences

In a premium auction, the seller offers some “payback”, called premium, to a set of high bidders at the end of the auction. This paper investigates how the performance of such premium tactics is related to the biddersʼ risk preferences. We analyze a two-stage English premium auction model with symmetric interdependent values, in which the bidders may be risk averse or risk preferring. Upon establishing the existence and uniqueness of a symmetric equilibrium, we show that the premium causes the expected revenue to increase in the biddersʼ risk tolerance. A “net-premium effect” is key to this result.

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

This paper analyzes the effects of buyer and seller risk aversion in first and second-price 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 first-price auction. Thus, greater seller risk aversion increases the ex post efficiency of both auctions, and especially that of the first-price auction. The seller’s optimal reserve price in the first-price, but not in the second-price, auction decreases in the buyers’ risk aversion. Thus, greater buyer risk aversion also increases the ex post efficiency of the first but not the second-price auction. At the interim stage, the first-price auction is preferred by all buyer types in a lower interval, as well as by the seller.

How Risk Sharing May Enhance Efficiency in English Auctions

We investigate the possibility of enhancing efficiency by awarding premiums to a set of highest bidders in an English auction— in a setting that extends Maskin and Riley (1984, Econometrica 52: 1473-1518) in three aspects: (i) the seller can be risk averse, (ii) the bidders can have heterogeneous risk preferences, and (iii) the auction can have a binding reserve price. Our analysis reveals that the premium has an intricate joint effect on risk sharing and expected revenue, which in general benefits risk averse bidders. When the seller is more risk averse than the pivotal bidder –a condition often verifiable by deduction prior to the auction –the premium also benefits the seller and therefore leads to a Pareto improvement of the English auction. We discuss how this finding is related to the seller’s degree of risk aversion, the reserve price, the riskiness of the object for sale, the degree of heterogeneity in risk preferences among the bidders, and the number of the potential bidders.