Bidders' Responses to Auction Format Change in Internet Display Advertising Auctions

Technical Summary: Bidders' Responses to Auction Format Change in Internet Display Advertising Auctions

Problem and Motivation
The paper investigates the empirical behavior of bidders when a market transitions from Second-Price Auctions (SPAs) to First-Price Auctions (FPAs). While classical auction theory (e.g., Vickrey 1961; Myerson 1981) predicts that rational bidders in SPAs bid their true valuations, whereas in FPAs they must optimally "shade" their bids (bid below their valuation) to balance winning probability against payment, the literature has largely relied on structural econometric models or laboratory experiments. There is a scarcity of field studies examining how bidders actually learn and adjust to such a fundamental market design change in real-time. The authors aim to fill this gap by analyzing the transition in the internet display advertising industry, where a significant shift from SPAs to FPAs occurred across major publishers.

Methodology
The study utilizes a novel, massive-scale dataset from Xandr (formerly AppNexus), covering hundreds of millions of daily auctions. The data is aggregated at the publisher–bidder–day level, recording sold impressions and aggregate revenue. The authors exploit a "staggered adoption" design where different publishers switched from SPAs to FPAs at four distinct points between September 2017 and June 2020.

The empirical strategy employs two primary econometric approaches:

1. Difference-in-Differences (DID): The authors estimate dynamic event-study regressions for four distinct treatment–control pairs. The outcome variable is the average price (revenue per sold impression). The models include publisher and time fixed effects, as well as publisher-specific seasonal controls (day of week, day of month, month, and end-of-quarter). The treatment effect is identified by comparing the price evolution of publishers switching to FPAs against those remaining in SPAs.
2. Synthetic Difference-in-Differences (SDID): To address potential violations of the parallel trends assumption, particularly given small numbers of treated units in some events, the authors implement the SDID estimator (Arkhangelsky et al. 2021). This method combines DID with synthetic control weighting, re-weighting control units and time periods to better match pre-treatment trends of the treated units.

The authors also conduct extensive robustness checks, including falsification tests with hypothetical event dates, alternative control group definitions, and analyses to rule out advertising campaign budget constraints as the primary driver of price changes.

Key Results

• Immediate Price Jumps: Immediately following the switch to FPAs, the average revenue per sold impression for treated publishers increased significantly relative to control publishers. The magnitude of this jump ranged from approximately 25% to 75% of the pre-treatment price level, depending on the specific event and specification.
• Transitory Nature and Learning: For three of the four format changes, the price increase was not permanent. The premium associated with FPAs relative to SPAs tended to dissipate over a period of 30 to 60 days. In some specifications, prices eventually converged back to levels statistically indistinguishable from the pre-treatment SPA levels.
• Bidder Heterogeneity: The study finds significant heterogeneity in responses based on bidder sophistication. When separating bidders into those using the ad exchange's native bidding algorithm ("AppNexus/Xandr bidder") and those using external algorithms ("naive" bidders), the latter group exhibited a much larger and more persistent price increase. The sophisticated bidder adjusted more quickly, shading bids more aggressively and immediately, suggesting that the initial price surge was driven by insufficient bid shading from less sophisticated participants.
• Budget Constraints: The authors find limited evidence that fixed advertising budgets drove the results. The volume of impressions sold did not mechanically decrease in a way that would solely explain the price rise, and spending patterns across bidders showed high variability rather than fixed allocation to specific publishers.

Significance and Claims
The paper positions itself as one of the first field studies to document bidder responses to auction format changes, providing empirical evidence that complements theoretical predictions. The authors interpret their findings as evidence of initially insufficient bid shading followed by a gradual learning process.

Contrary to the immediate transition to a new Bayesian Nash equilibrium predicted by standard theory, the data suggests that bidders (particularly those without sophisticated algorithms) initially fail to shade their bids optimally when moving from SPAs to FPAs, causing a temporary price spike. Over time, as bidders learn the new environment, prices adjust downward.

The authors note that the eventual convergence of FPA and SPA prices is reminiscent of the Revenue Equivalence Theorem, even though the strict prerequisites for that theorem (such as bidder symmetry) do not hold in this setting. They caution market designers that while a format change may appear to increase revenue in the short run due to suboptimal bidding, this effect may dissipate as the market matures and bidders learn to bid optimally. The work serves as a valuable complement to theoretical models, highlighting the importance of learning dynamics in real-world auction markets.