Pacing Equilibrium in First-Price Auction Markets

In the isolated auction of a single item, second price is often preferable to first price in properties of theoretical interest. Unfortunately, single items are rarely sold in true isolation, so considering the broader context is critical when adopting a pricing strategy. In this paper, we show that this context is important in a model centrally relevant to Internet advertising: when items (ad impressions) are individually auctioned within the context of a larger system that is managing budgets, theory offers surprising support for using a first price auction to sell each individual item. In particular, first price auctions offer theoretical guarantees of equilibrium uniqueness, monotonicity, and other desirable properties, as well as efficient computability as the solution to the well-studied Eisenberg-Gale convex program. We also use simulations to demonstrate that while there are incentives to misreport in thin markets (where budgets aren't constraining), a bidder's incentive to deviate vanishes in thick markets.