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arXiv · 2609.34515

Nash Equilibria in Auctions with Pacing Strategies: Complexity and Inefficiency

Aris Filos-Ratsikas·Charalampos Kokkalis·Mohamad Latifian
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Abstract

We introduce and study Auctions with Pacing Strategies (APS) games, a full-information model in which utility-maximizing bidders compete across many simultaneous first-price auctions, each choosing a single pacing multiplier that uniformly scales their values into bids. We settle three central questions. First, we show that there are instances that admit no approximate pure Nash equilibria. Then, we prove that the problem of deciding whether an APS game admits an (approximate) equilibrium is NP-complete in general, but can be solved in polynomial time if either the number of bidders or the number of items is fixed. Finally, when an equilibrium does exist, we characterize its inefficiency exactly, showing that both the Price of Anarchy and the Price of Stability equal $\frac{e}{e-1}$.

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Aris Filos-Ratsikas, Charalampos Kokkalis, Mohamad Latifian. 2026-09-28. Nash Equilibria in Auctions with Pacing Strategies: Complexity and Inefficiency. https://arxiv.org/abs/2609.34515

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