Why Do Competitive Markets Converge to First-Price Auctions?

We consider a setting in which bidders participate in multiple auctions run by different sellers, and optimize their bids for the aggregate auction. We analyze this setting by formulating a game between sellers, where a seller's strategy is to pick an auction to run. Our analysis aims to shed light on the recent change in the Display Ads market landscape: here, ad exchanges (sellers) were mostly running second-price auctions earlier and over time they switched to variants of the first-price auction, culminating in Google's Ad Exchange moving to a first-price auction in 2019. Our model and results offer an explanation for why the first-price auction occurs as a natural equilibrium in such competitive markets.