Risk Sharing, Effi ciency, and English Premium Auctions1

1 This paper has bene…ted from communications with Steve Matthews on related issues. and suggestions. Any remaining errors are our own. A de…ning feature of the premium auctions is that the seller commits to o¤ering a share of pro…t, called " premium, " to a number of highest bidders when the auction ends successfully. This paper analyzes an English premium-auction (EPA) model 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 reserve price. Our analysis reveals that the premium has a general joint e¤ect on risk sharing and expected revenue. A su¢ cient condition for the seller to prefer the EPA to the standard English auction is that he is more risk averse than the pivotal bidder. Ex ante, this condition can be veri…ed by deduction using the reserve price. Under this condition, when both the seller and bidders are risk averse the premium improves ex ante Pareto e¢ ciency by making all players better o¤. We show that the advantage of the premium tactics is directly related to (a) the seller's degree of risk aversion, (b) the reserve price, (c) the riskiness of the object for sale, (d) the degree of heterogeneity in risk preferences among the bidders, and (e) the number of the potential bidders.