How Risk Sharing May Enhance Efficiency in English Auctions

Abstract

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.