Sniping in Proxy Auctions with Deadlines

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