# Correlated and Coarse equilibria of Single-item auctions

arXiv: https://arxiv.org/abs/1601.07702 · HTML: https://mlsanity.com/paper/1601.07702/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Jan 2016.

## Built on by (most cited first, 8 of 8)

- [Contracting with a Learning Agent](https://mlsanity.com/paper/2401.16198/) (2024)
- [Auctions Between Regret-Minimizing Agents](https://mlsanity.com/paper/2110.11855/) (2021)
- [The Role of Transparency in Repeated First-Price Auctions with Unknown Valuations](https://mlsanity.com/paper/2307.09478/) (2023)
- [Learning in Repeated Multi-Unit Pay-As-Bid Auctions](https://mlsanity.com/paper/2307.15193/) (2023)
- [Games with Payments between Learning Agents](https://mlsanity.com/paper/2405.20880/) (2024)
- [Proximal Regret and Proximal Correlated Equilibria: A New Tractable Solution Concept for Online Learning and Games](https://mlsanity.com/paper/2511.01852/) (2025)
- [Breaking Algorithmic Collusion in Human-AI Ecosystems](https://mlsanity.com/paper/2511.21935/) (2025)
- [Revisiting the Bertrand Paradox via Equilibrium Analysis of No-regret Learners](https://mlsanity.com/paper/2602.21620/) (2026)

## Abstract (arXiv)

We study correlated equilibria and coarse equilibria of simple first-price single-item auctions in the simplest auction model of full information. Nash equilibria are known to always yield full efficiency and a revenue that is at least the second-highest value. We prove that the same is true for all correlated equilibria, even those in which agents overbid -- i.e., bid above their values. Coarse equilibria, in contrast, may yield lower efficiency and revenue. We show that the revenue can be as low as 26% of the second-highest value in a coarse equilibrium, even if agents are assumed not to overbid, and this is tight. We also show that when players do not overbid, the worst-case bound on social welfare at coarse equilibrium improves from 63% of the highest value to 81%, and this bound is tight as well.