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

2026-06-04

AI Summary

This study addresses revenue guarantees in discrete first-price auctions under no-swap-regret dynamics, focusing on approximate correlated equilibria. Considering a discretized bidding space $\{0, 1/k, \dots, 1\}$, the work establishes—by integrating concepts from correlated equilibrium and swap regret analysis—the first polynomial-rate convergence of revenue toward the second-highest valuation. The main contribution is a rigorous bound showing that the revenue of any $\varepsilon$-approximate correlated equilibrium is at least $v_2 - \Theta(1/k) - \Theta(\varepsilon k^2)$. Furthermore, it demonstrates that after $O(k^5 / \varepsilon^2)$ rounds, the time-averaged revenue approaches the second-highest value, thereby providing theoretical assurance of revenue stability for discrete auction mechanisms.

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 $ε$-approximate correlated equilibrium is at least $v_2 - Θ(1/k)- Θ(εk^2)$, 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 $v_2 - Θ(1/k) - Θ(ε)$ after $\mathcal{O}(k^5/ε^2)$ rounds.

Problem

• revenue guarantees
• first price auctions
• no-swap regret
• correlated equilibrium
• auction dynamics

Innovation

• no-swap regret
• first-price auctions
• revenue guarantee
• approximate correlated equilibrium
• convergence rate