Comparing Auctions for Risk Averse Buyers: A Buyer's Point of View

THE SELLER'S POINT OF VIEW is the predominant one taken in the literature. Much attention, for example, has been given to revenue equivalence theorems that state conditions under which a seller is indifferent between various types of auctions,3 and optimal auction theorems that characterize auctions which maximize the seller's expected profit.4 To offset this bias, in this paper auctions are compared from the point of view of the buyers. The first comparison is of a first-price (FPA), in which the high bidder wins and is charged a price equal to his own bid, to a second-price (SPA), in which the high bidder wins and is charged a price equal to the second highest bid. It is well-known that if the buyers are risk averse and have private i.i.d. values, each bidder's expected payment is greater in the FPA.5 A buyer nevertheless need not prefer the SPA, since his payment is a riskier random variable in the SPA than it is in the FPA.6 The two effects can exactly counteract each other: in Section 2 buyers with private i.i.d. values who exhibit constant absolute risk aversion (CARA) are shown to be indifferent between the two auctions. Thus,