Gradual Bidding in Ebay-Like Auctions

This paper shows that in online auctions like eBay, if bidders can only place bids at random times, then many di fferent equilibria arise besides truthful bidding, despite the option to leave proxy bids. These equilibria can involve gradual bidding, periods of inactivity, and waiting to start bidding towards the end of the auction - bidding behaviors common on eBay. Bidders in such equilibria implicitly collude to keep the increase of the winning price slow over the duration of the auction. In a common value environment, we characterize a class of equilibria that include the one in which bidding at any price is maximally delayed, and all bids minimally increment the price. The seller's revenue can be a small fraction of what could be obtained at a sealed-bid second-price auction, and in the worst equilibrium it is decreasing in the value of the object. With many bidders, we show that this equilibrium has the feature that bidders are passive until near the end of the auction, and then they start bidding incrementally.