  The internet advertising market is a multi-billion dollar industry, in which
advertisers buy thousands of ad placements every day by repeatedly
participating in auctions. An important and ubiquitous feature of these
auctions is the presence of campaign budgets, which specify the maximum amount
the advertisers are willing to pay over a specified time period. In this paper,
we present a new model to study the equilibrium bidding strategies in standard
auctions, a large class of auctions that includes first- and second-price
auctions, for advertisers who satisfy budget constraints on average. Our model
dispenses with the common, yet unrealistic assumption that advertisers' values
are independent and instead assumes a contextual model in which advertisers
determine their values using a common feature vector. We show the existence of
a natural value-pacing-based Bayes-Nash equilibrium under very mild
assumptions. Furthermore, we prove a revenue equivalence showing that all
standard auctions yield the same revenue even in the presence of budget
constraints. Leveraging this equivalence, we prove Price of Anarchy bounds for
liquid welfare and structural properties of pacing-based equilibria that hold
for all standard auctions. In recent years, the internet advertising market has
adopted first-price auctions as the preferred paradigm for selling advertising
slots. Our work thus takes an important step toward understanding the
implications of the shift to first-price auctions in internet advertising
markets by studying how the choice of the selling mechanism impacts revenues,
welfare, and advertisers' bidding strategies.
