Pacing Equilibrium in First-Price Auction Markets

Abstract

In the isolated auction of a single item, second price often dominates first price in properties of theoretical interest. But, single items are rarely sold in true isolation, so considering the broader context is critical when adopting a pricing strategy. In this paper, we study a model centrally relevant to Internet advertising and show that when items (ad impressions) are individually auctioned within the context of a larger system that is managing budgets, theory offers surprising endorsement 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 a bidder's incentive to deviate vanishes in thick markets. *

The Complexity of Pacing for Second-Price Auctions

“…The appropriate notion of equilibrium in this game is the pacing equilibrium.In this work, we show that the problem of nding an approximate pacing equilibrium is PPAD-complete for second-price auctions. This resolves an open question of [2]. As a consequence of our hardness result, we show that the tatonnement-style budget-management dynamics introduced by [1] is unlikely to converge e ciently for repeated second-price auctions.…”

Causal Models for Real Time Bidding with Repeated User Interactions

“…The bidder now needs to estimate the distribution of the price to beat -the highest bid of the competition -to compute its optimal bid [Krishna, 2009]. Second, it is common for the bidder to have some constraints on the advertising campaign, such as a maximum budget per day, or a maximum cost per click [Conitzer et al, 2018, Heymann, 2019. While in several cases a linear scaling applied to the display valuation may be enough to optimally satisfy a budget constraint, the value of this scaling factor is not known in advance, and several articles propose to update the bidding strategy to better take such constraint into account [Cai et al, 2017, Grislain et al, 2019, Lee et al, 2013, Yang et al, 2019.…”

How to bid in unified second-price auctions when requests are duplicated

“…In [18], Balseiro et al study the impact of budget constraints on advertiser behavior by combining queuing theory and mean field approaches. The notion of pacing algorithms [19,20] emerged from the need to dynamically implement such business constraints. Heymann [21] provides an analysis of the impact of CPA constraints in the buyer optimisation problem on the market outcomes.…”