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arXiv · 2605.09332

Pacing Equilibria in Second-Price Auctions with Few Goods

Yiyang Huang·Yonglei Yan·Zihe Wang·Zhengyang Liu
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Abstract

In this paper, we investigate the computation of second-price pacing equilibria (SPPEs), a foundational model in online advertising auctions. We present a polynomial-time algorithm for computing exact SPPEs in instances with a constant number of goods. Our core technique maps buyers' pacing multipliers to the highest bids on each good, effectively partitioning the parameter space into a set of distinct geometric cells. By enumerating these cells, we fix the relative ordering of the bids and reduce the problem of equilibrium computation to a linear feasibility program. Finally, we demonstrate that this tractability extends to large-scale markets with an arbitrary number of goods, provided the goods can be aggregated into a constant number of valuation types.

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Yiyang Huang, Yonglei Yan, Zihe Wang, Zhengyang Liu. 2026-05-10. Pacing Equilibria in Second-Price Auctions with Few Goods. https://arxiv.org/abs/2605.09332

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