Adjustment of Bidding Strategies After a Switch to First-Price Rules

We document the response of bidders to a change in auction pricing rules by a platform selling online advertising impressions. The platform switched from a second-price auction to a first-price auction in 2019. We analyze the transition and ask three questions: Did the bids by the same bidder bidding to show the same creative in the same location on the same webpage fall? If yes, did the bids fall enough? And if the bids fell enough, how long did the transition take? To answer our questions, we study 11 long-running creatives with sufficient volume of bids for a month before the switch and three months after the switch. We find that bids on these long-running creatives indeed declined after the switch, but this decline was not sufficient. To detect insufficient shading, we propose a simple nonparametric estimator of the lower bound on advertiser valuations in first-price sealed-bid auctions. Unlike standard econometric approaches to first-price auctions, our bound estimator does not assume equilibrium and it can accommodate affiliated private values. The identifying assumption is that each bidder prefers his actual bid to an even lower bid given the hyper-local competition the bidder is facing at the moment. This assumption implies a lower bound on a rationalizable valuation of the bidder in a first-price auction. Comparing the post-switch valuation lower bounds to the pre-switch valuation magnitudes allows us to detect insufficient adjustment whenever the former exceeds the latter. And we indeed find that the bid shading was insufficient for a vast majority of bidders and creatives included in our study: observed bids on the median creative imply that the bidder bid as if the switch from second-price to first-price rules increased his valuation of an impression at least 30 percent. We also find evidence of an incomplete and slow downward adjustment in bid magnitude over the period of months, whereby bids remain insufficiently shaded for about half of the creatives even three months after the switch. The full paper is available at: https://ssrn.com/abstract=4036006