Uniqueness of equilibrium in sealed high - bid auctions ✩ Eric Maskin

For the case of two buyers we show that equilibrium in the sealed high-bid auction is unique when (i) buyers’ reservations prices are drawn independently from distributions with finite support and positive mass at the lower endpoint; (ii) buyers have private values; and (iii) buyers’ preferences are log supermodular. For more than two buyers, we obtain the same result under the additional assumptions that (iv) buyers with the same reservation price have the same preferences; (v) buyers are risk neutral or risk averse with non-increasing absolute risk aversion; and (vi) the supports of the different buyers’ distributions of reservation prices have the same upper endpoint.  2003 Elsevier Inc. All rights reserved. JEL classification: D44; D82