  Mature internet advertising platforms offer high-level campaign management
tools to help advertisers run their campaigns, often abstracting away the
intricacies of how each ad is placed and focusing on aggregate metrics of
interest to advertisers. On such platforms, advertisers often participate in
auctions through a proxy bidder, so the standard incentive analyses that are
common in the literature do not apply directly. In this paper, we take the
perspective of a budget management system that surfaces aggregated incentives
-- instead of individual auctions -- and compare first and second price
auctions. We show that theory offers surprising endorsement for using a first
price auction to sell individual impressions. In particular, first price
auctions guarantee uniqueness of the steady-state equilibrium of the budget
management system, monotonicity, and other desirable properties, as well as
efficient computation through the solution to the well-studied Eisenberg-Gale
convex program. Contrary to what one can expect from first price auctions, we
show that incentives issues are not a barrier that undermines the system. Using
realistic instances generated from data collected at real-world auction
platforms, we show that bidders have small regret with respect to their optimal
ex-post strategy, and they do not have a big incentive to misreport when they
can influence equilibria directly by giving inputs strategically. Finally,
budget-constrained bidders, who have significant prevalence in real-world
platforms, tend to have smaller regrets. Our computations indicate that bidder
budgets, pacing multipliers and regrets all have a positive association in
statistical terms.
