Journal of Economic Theory 112 (2003) 261–288 Asymmetric English auctions Vijay Krishna Department of Economics, Penn State University, University Park, PA 16802, USA Received 28 February 2001; final version received 7 August 2002 Abstract This paperstudiesequilibria ofthe n-biddersingle-object English,or open ascending price,auction in a setting with interdependent values and asymmetric bidders. Maskin (in: H. Siebert (Ed.), Privatization, Institut fur Weltwirtschaften der Universita ¨t Kiel, Kiel, 1992, pp. 115–136.) showed that if the values satisfy a ‘‘single crossing’’ condition,then the two- bidder English auction has an efficient equilibrium. In this paper, two extensions of the sing crossing condition, the ‘‘average crossing’’ condition and the ‘‘cyclical crossing’’ condition, introduced. The main result is that under either of these conditions the n-bidder English auction has an efficient equilibrium. r 2003 Elsevier Science (USA). All rights reserved. JEL classification: D44; D82 Keywords: Auctions; Efficiency 1. Introduction The English, or open ascending price, auction is the oldest and perhaps the most prevalent auction mechanism. Indeed,the word auction itself is derived from the Latin augere, which means ‘‘to increase.’’ Beginning with the pioneering work of Vickrey [18], the English auction has been the subject of extensive study in the analysis of auctions as games of incomplete information. In the private values mod introduced by him, Vickrey [18] observed that the English auction always allocates the object efficiently whereas, when bidders are asymmetric, the first-price sealed- auction may not. ARTICLE IN PRESS Fax: +1-814-863-4775. E-mail address: vkrishna@psu.edu. 0022-0531/03/$ - see front matter r 2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0022-0531(03)00074-7