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arXiv · 2606.06085

Revenue Guarantees of No-Swap-Regret Dynamics in First Price Auctions

Anders Bo Ipsen·Stratis Skoulakis
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Abstract

We study the revenue of approximate correlated equilibrium in discrete first price auctions - the set of allowable bids is $\mathcal{B} = \{0, 1/k, \dots, 1 - 1/k, 1\}$ for some $k \in \mathbb{N}$. We show that the revenue of any $\epsilon$-approximate correlated equilibrium is at least $v_2 - \Theta(1/k)- \Theta(\epsilon k^2)$, where $v_2 \geq 0$ is the second-highest valuation. Our results establish the first polynomial convergence rates on the revenue generated by no-swap regret bidders in first-price auctions. For instance, if bidders admit the optimal swap regret of $\mathcal{O}(\sqrt{k T})$, then the time-averaged revenue is at least $v_2 - \Theta(1/k) - \Theta(\epsilon)$ after $\mathcal{O}(k^5/\epsilon^2)$ rounds.

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Anders Bo Ipsen, Stratis Skoulakis. 2026-06-04. Revenue Guarantees of No-Swap-Regret Dynamics in First Price Auctions. https://arxiv.org/abs/2606.06085

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