  We consider a setting in which bidders participate in multiple auctions run
by different sellers, and optimize their bids for the \emph{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.
