  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. In recent years, the industry has shifted to
first-price auctions as the preferred paradigm for selling advertising slots.
Another 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 first-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, and
study its structural properties. Furthermore, we generalize the existence
result to standard auctions and prove a revenue equivalence showing that all
standard auctions yield the same revenue even in the presence of budget
constraints.
