Bid Shading in Dynamic Auctions

We develop a dynamic model of bidding where agents’ values follow a joint Markov process. Agents can bid at different times in the auction. The paper considers a baseline case where an exogenous random process gives bidding times and in addition a simplified scenario with endogenous rebidding and menu costs. For the case of exogenous rebidding, we prove that equilibrium exists and is unique, providing a recursive representation and algorithm to solve for bids as a function of time and values. The equilibrium bid equals the expected final value conditional on being the bidder's final one: either there is no further rebidding opportunity or the bidder chooses not to increase this bid if given the option. This is lower than the unconditional expected value; so early bids are shaded and increase over time as the close of the auction is approached. We consider identification of the model and estimate parameters. The resulting distribution of winning bids in the model is considerably skewed towards the later part of the auction, as is also found in the data. Our results are consistent with repeated bidding and sniping, two puzzling observations in eBay auctions. We consider a series of counterfactuals.