Budget-Management Strategies in Repeated Auctions

In online advertising, advertisers purchase ad placements by participating in a long sequence of repeated auctions. One of the most important features that advertising platforms often provide and advertisers often use is budget management, which allows advertisers to control their cumulative expenditures. Advertisers typically declare the maximum daily amount they are willing to pay, and the platform adjusts allocations and payments to guarantee that cumulative expenditures do not exceed budgets. There are multiple ways to achieve this goal, and each one, when applied to all budget-constrained advertisers simultaneously, drives the system toward a different equilibrium. Our goal is to compare the “system equilibria” of a range of budget-management strategies. In particular, we consider six different budget-management strategies, including probabilistic throttling, thresholding, bid shading, reserve pricing, and two versions of multiplicative boosting. We show that these methods admit a system equilibrium, study their incentive properties, prove dominance relations among them in a simplified setting, and confirm our theoretical findings using real ad auction data from a sponsored search. Our study sheds light on the impact of budget-management strategies on the trade-off between the seller’s profit and buyers’ utility and may be of practical relevance for advertising platforms.