In the past few years, we have witnessed a tremendous proliferation of transactions using the Internet as a virtual marketplace. U.S. News and World Report estimates the value of electronic commerce around $13 billion in 1998. In addition to transactions where prices are posted, sellers also use Internet auctions to sell goods such as clothing, collectibles, computers, and electronics. Current estimates place the value of auction transactions in the Internet at $30 million per week. A popular format for Internet auctions is the Yankee format. Here, a seller offers k identical units for sale, and bidders specify how many units they want and the per-unit price they want to pay. Bidding takes place progressively over a predetermined time period and the k highest bids at closing win the units at their specified prices. Ties are broken on the basis of quantities first and time of bidding second. Two features make these auctions different from standard auctions. First, unlike "live" auctions with fixed participation costs, entering each bid may be costly in a Yankee auction since bidding takes place over several hours (or days) and, in addition to connectivity cost, several minutes time must spend several registering the new price. Second, each time the bidder visits the auction site, she is uncertain about the competition since it is possible for more bidders to decide to enter before the closing. Here, we derive and characterize equilibrium strategies in simple Yankee auctions with stochastic demand. We show that costly bidding may induce bidders to bid high or jump bid in earlier rounds. These jump bids play a signaling role; they attempt to discourage later bidders from competing with established bidders. This way, under some conditions, both sender and receiver of the signal may be better off in equilibrium. The sender because deterring competition saves her the costs of additional bids, and the receiver because she avoids the costs of fruitless early competition. Here, we derive conditions on bidding costs and bidder types that result in a signaling equilibrium of this nature. We show that the characteristics of the equilibrium are closely related to the structure of demand uncertainty faced by the bidders since signal bidding has more strategic value when bidders anticipate further competition later in the auction. We use data from hundreds of Yankee Auctions to test some predictions of the jump-bidding model. In confirmation, we find (a) over 40% of the bidders in our sample enter jump bids, (b) any individual bidder is more likely to enter a jump bid as his first bid, (c) earlier bidders are more likely to enter jump bids than later bidders, (d) the relative size of a jump bid is increasing in the number of bidders relative to units being sold, and (e) the relative size of a jump bid is decreasing in the object's average value. We conclude with a discussion of the implications of costly bidding and jump-bidding strategies on Internet auction design.
