Late Bidding in Open Auctions with Two Bidders

In open internet auctions with deadlines, some bids made near the deadline are randomly lost. Roth and coauthors have demonstrated via full-information examples that multiple bidders bidding late can nevertheless be equilibrium behavior, as the cost to one bidder of a lost bid can be outweighed by the gain when others’ bids are lost. We extend to a standard symmetric two-bidder environment with continuously distributed random private values. For strategies in which every type of bidder either bids immediately, or waits to bid late when the other bidder has done so, all equilibria are symmetric. In any equilibrium in which some types bid late, those that bid late are an interval that includes the lowest type. Equilibria in which at least some types bid late exist when the probability of a lost bid is small, and when buyer values are probabilistically high.