“…One is search auction, denoted by A s , where a seller incurs costs to attract bidders to the auction (Crémer, et al 2007;Szech, 2011;Li and Xu, 2016). The other is auctions with costly entry, where bidders need to pay entry costs to participate in the auction, which can be further summarized to two branches: in the …rst branch, denoted by A u , bidders make entry decisions before knowing their true valuations of the product (McAfee and McMillan, 1987;Levin and Smith, 1994) (Samuelson, 1985;Tan and Yilankaya, 2006;Cao and Tian, 2010).…”