Auctions are a popular and prevalent form of trading mechanism, despite the restriction that the seller cannot price-discriminate among potential buyers. To understand why this is the case, we consider an auction-like environment in which a seller with an indivisible object negotiates with two asymmetric buyers to determine who obtains the object and at what price. The trading process resembles the Dutch auction, except that the seller is allowed to offer different prices to different buyers. We show that when the seller can commit to a price path in advance, the optimal outcome can generally be implemented. When the seller lacks such commitment power, however, there instead exists an equilibrium in which the seller's expected payoff is driven down to the second-price auction level. Our analysis suggests that having the discretion to price discriminate is not necessarily beneficial for the seller, and even harmful under plausible conditions, which could explain the pervasive use of auctions in practice.