Time-Varyingness in Auction Breaks Revenue Equivalence

The revenue equivalence theorem states that equilibrium revenue is the same across different auction mechanisms, such as first- and second-price ones. However, the environment in the real-world auctions varies over time and can prevent bidders from reaching such an equilibrium. While second-price auctions allow bidders to automatically maintain equilibrium through truthful bidding, first-price auctions require bidders to track moving equilibria through continuous learning. We demonstrate that this tracking lag breaks revenue equivalence. Which of the first- and second-price auctions yields higher revenue depends on the correlation between the basis value (the standard price to bid) and the value interval (the width of possible values). This study uncovers a novel phenomenon that can be triggered by time-varying environments in real-world auctions.