Late and Multiple Bidding in Second-Price Internet Auctions
As we discussed in class, second-price auctions are ubiquitous on the internet: the highest bidder wins the item but but pays the second-highest bid. Amazon and eBay both use this model of auction. Authors Ockenfels and Roth noted that eBay auctions are more likely to have many late bidders, who put in their bids shortly before the fixed bidding time is about to expire in an effort to “snipe” the item. They also observe multiple bidding, where bidders submit multiple bids during the course of the auction. Curiously, the tendency of bidders to input late or multiple bids goes against the advice of auctioneers, who urge bidders to put in a single, early bid. As we learned in class, the bidder’s strictly dominant strategy is to bid his or her true value, so we do not expect late or multiple bids to give the bidders an advantage in the auction. Furthermore, as any internet user knows, trying to snipe an item is risky: increased internet traffic on the site shortly before the bid closes could mean that the website fails to load on time and the bidder is unable to submit his bid in time. Consequently, even websites like esnipe.com, which is designed to submit a bid for you seconds before bidding time expires, acknowledge that there is a nonzero probability of that bid being lost.
Ockenfels and Roth show that this daredevil approach to bidding actually has powerful incentives in fixed-deadline auctions. To justify their claim, they analyze data from both Amazon and eBay auctions. eBay is a fixed-deadline auction, while Amazon extends the length of the auction so that bidding will only end a full ten minutes after the final bid is placed. They show that late-bidding is a best response to so-called naïve bidding in an eBay-type auction, but not in an Amazon-style auction without a fixed deadline. Indeed, experienced eBay bidders submit their bids late. As it turns out, bidders who submit only one bid also tend to be more experienced than those that submit multiple bids.
The authors construct a model of the eBay-style second price auction. There are n bidders and the bidding starts off at an initial price m. There is a smallest increment, s, by which subsequent bids can raise the price. Each submitted price must exceed the current price and the corresponding bidder’s last submitted price, so no one may subsequently lower a bid. They also add some technicalities to their model about the time interval in which bidders may bid such that the bidders have time to respond to eachother’s bids. They then prove a theorem that says “A bidder in the second price eBay-model auction with private values does not have any dominant strategies, as long as his value is greater than m+s”. This result sounds strange to us Networks students, since we have seen that bidding one’s true value in second price auctions is a dominant strategy! They go on to prove that bidding at a late time can be a best response to incremental bidding. I refer the interested reader to the source material for the details of the proofs. It is important to note that their proofs rely on both “rational” bidders and “incremental” bidders participating in the auction. The rational bidder is a strategist that is prepared to use late bidding to win the item, while the incremental bidders mechanically raise their bid at various timesteps throughout the auction until they drop out. The authors prove that these rational bidders can best respond to the incremental bidders, but they do not prove that rational bidders can best respond to other rational bidders by late bidding. The authors even go on to show that sniping can be equilibrium behavior in common value, as well as private value, auctions.
It is important to note that these results do not fly in the face of what we learned in the course. If you are bidding on a popular item against not only incremental bidders but other rational bidders, you may not want to bid too early if that will incite a bidding war over the item that will rapidly raise the price of the good. If you bid late, an incremental bidder may not have time to push the price up above your new bid before the auction ends. In spite of these complications, the rational bidder is still bidding his or her true value, whether the bid is placed early or late. Rather, the details of the auction type just add a new parameter to your best response: time of bid. And don’t forget, bidding late has an associated risk, even though it may be a best response strategy!