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 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, steers the system toward a different equilibrium. While previous research focused on online stochastic optimization techniques or game-theoretic equilibria of such settings, our goal in this paper is to compare the ``system equilibria'' of a range of budget management strategies in terms of the seller's profit and buyers' utility. In particular, we consider six different budget management strategies including probabilistic throttling, thresholding, bid shading, reserve pricing, and multiplicative boosting. We show these methods admit a system equilibrium in a rather general setting, and prove dominance relations between them in a simplified setting. Our study sheds light on the impact of budget management strategies on the tradeoff between the seller's profit and buyers' utility. Finally, we also empirically compare the system equilibria of these strategies using real ad auction data in sponsored search and randomly generated bids. The empirical study confirms our theoretical findings about the relative performances of budget management strategies.