Correlated and Coarse equilibria of Single-item auctions

TL;DR

This paper analyzes the efficiency and revenue outcomes of correlated and coarse equilibria in single-item first-price auctions, revealing that correlated equilibria maintain full efficiency and revenue, while coarse equilibria can significantly underperform.

Contribution

It demonstrates that correlated equilibria preserve full efficiency and revenue in first-price auctions, whereas coarse equilibria can lead to substantially lower outcomes, providing tight bounds for both scenarios.

Findings

Correlated equilibria always achieve full efficiency and revenue.

Coarse equilibria can reduce revenue to as low as 26% of the second-highest value.

When no overbidding occurs, social welfare at coarse equilibrium is at least 81%, tight bound.

Abstract

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.