June 2016
In most online auctions with deadlines, bidders submit multiple bids and wait until late in the auction to submit high bids, a practice popularly known as “sniping.” This paper shows that whenever there is a nonzero probability that an auction contains “shill bidders,” who attempt to raise the sale price without winning, equilibrium play must exhibit sniping. We present a model of online auctions with stochastic bidding opportunities and incomplete information regarding competing players’ valuations. We characterize perfect Bayesian equilibria under a trembling hand refinement, allowing for a positive probability that a player is a bidder who plays a fixed strategy that raises the sale price. In doing so, we develop a one-shot deviation principle for a class of continuous-time games with stochastic opportunities to move. We find that in all equilibria, players wait until a late time threshold to place their bids, even as the probability that a shill bidder is present becomes arbitrarily small. Using data from eBay auctions, we show that observed behavior is consistent with equilibrium play and that comparative statics of the timing of bids match the model’s predictions. In contrast, when there is no possibility of a shill bidder, the unique equilibrium outcome is that players bid their valuation as soon as a bidding opportunity arrives. The results extend to other types of heuristic bidders who place incremental bids.