Two-Stage Buy-It-Now Auctions

This paper studies auctions with a temporary Buy-It-Now (BIN) price using a two-stage model. In the first stage, a group of bidders (early bidders) are offered a ”Buy-It-Now” (BIN) option to purchase the item immediately at a listed price (BIN price). If no early bidder accepts the BIN price, the BIN option disappears and the second stage starts with an additional group of bidders (late bidders). Both early and later bidders then participate in a second-price sealed-bid auction. We establish that when bidders are risk neutral or risk averse, if the seller sets the BIN price low enough, an early bidder will accept the BIN price only if his valuation is higher than a unique equilibrium cutoff valuation. Other things being equal, the cutoff valuation decreases as bidders’ degree of risk aversion increases and increases as the number of early bidders increases. We found that facing risk neutral bidders, the seller sets a BIN price high enough such that no bidder will accept it thus the seller revenue is the same as in a second-price sealed-bid auction without a BIN pirce. When bidders are risk averse, by setting an appropriate BIN price, the seller can obtain a higher expected revenue in a two-stage BIN auction than in a standard second-price sealed-bid auction with the same reserve price, and the expected revenue increases as the number of early bidders decreases. These results may help explain the popularity of temporary BIN auctions in online auction sites such as eBay. ∗Department of Economics, Texas A&M University ([email protected])