Publication

Multiplicative Pacing Equilibria in Auction Markets

Operations Research Journal


Abstract

Budgets play a significant role in real-world sequential auction markets such as those implemented by internet companies. To maximize the value provided to auction participants, spending is smoothed across auctions so budgets are used for the best opportunities. Motivated by a mechanism used in practice by several companies, this paper considers a smoothing procedure that relies on pacing multipliers: on behalf of each buyer, the auction market applies a factor between 0 and 1 that uniformly scales the bids across all auctions. Reinterpreting this process as a game between buyers, we introduce the notion of pacing equilibrium, and prove that they are always guaranteed to exist. We demonstrate through examples that a market can have multiple pacing equilibria with large variations in several natural objectives. We show that pacing equilibria refine another popular solution concept, competitive equilibria, and show further connections between the two solution concepts. Although we show that computing either a social-welfare-maximizing or a revenue-maximizing pacing equilibrium is NP-hard, we present a mixed-integer program (MIP) that can be used to find equilibria optimizing several relevant objectives. We use the MIP to provide evidence that: (1) equilibrium multiplicity occurs very rarely across several families of random instances, (2) static MIP solutions can be used to improve the outcomes achieved by a dynamic pacing algorithm with instances based on a real-world auction market, and (3) for the instances we study, buyers do not have an incentive to misreport bids or budgets provided there are enough participants in the auction.

Related Publications

All Publications

ICML - July 24, 2021

Using Bifurcations for Diversity in Differentiable Games

Jonathan Lorraine, Jack Parker-Holder, Paul Vicol, Aldo Pacchiano, Luke Metz, Tal Kachman, Jakob Foerster

UAI - July 23, 2021

High-Dimensional Bayesian Optimization with Sparse Axis-Aligned Subspaces

David Eriksson, Martin Jankowiak

ICML - July 18, 2021

Barlow Twins: Self-Supervised Learning via Redundancy Reduction

Jure Zbontar, Li Jing, Ishan Misra, Yann LeCun, St├ęphane Deny

ICLR - September 16, 2020

Captum: a Unified and Generic Model Interpretability Library for PyTorch

Narine Kokhlikyan, Vivek Miglani, Miguel Martin, Edward Wang, Bilal Alsallakh, Jonathan Reynolds, Alexander Melnikov, Natalia Kliushkina, Carlos Araya, Siqi Yan, Orion Reblitz-Richardson

To help personalize content, tailor and measure ads, and provide a safer experience, we use cookies. By clicking or navigating the site, you agree to allow our collection of information on and off Facebook through cookies. Learn more, including about available controls: Cookies Policy