Dynamic Bidding in Second Price Auction

We consider equilibrium bidding behavior in a dynamic second price auction where agents have the option to increase bids at random times and values follow a Markov process. We prove that equilibrium exists and is unique and give an algorithm to solve for bids as a function of time and values. Equilibrium bids equal the expected final value conditional on the bid placed being the final one, meaning that either the agent doesn’t get another opportunity to rebid or chooses not to increase this bid if given the option. This results in adverse selection with respect to a bidder’s own future strategy, and as a result bids are shaded relative to the bidder’s expected value. This is true in spite of values being independent across bidders. Under mild conditions, desired bids increase as time increases and the close of the auction is approached. Our results are consistent with repeated bidding and sniping, two puzzling observations in eBay auctions. We estimate the model by matching moments from Ebay auctions and consider a series of counterfactuals. ∗[email protected] †[email protected] 1 ...if something went over my limit early on, I might re-evaluate my budget and make a higher bid because I want the product. If it was the last few minutes I wouldn’t have the time to consider if I can afford it. ...work + college = does not give you the right time you need to baby an auction. The wife wanted to go to lunch right at the same time as the end of the auction, so I decided to drop an early bid an hour before the close.