An empirical study of Fictitious Play for estimating Nash equilibria in first-price auctions with correlated values

2026-06-15

AI Summary

This work addresses the challenge of computing Nash equilibria in first-price auctions under value interdependence, a setting where existing methods often perform poorly. The paper presents the first successful application of Fictitious Play to this problem, introducing an iterative learning–based numerical algorithm that effectively approximates ε-Nash equilibria. Extensive experiments across diverse value interdependence structures demonstrate the algorithm’s strong convergence properties, indicating that Fictitious Play can efficiently handle equilibrium computation in such complex auction environments. These findings offer a novel computational tool for mechanism design in settings with interdependent valuations.

Abstract

This study concerns the computation of the Nash equilibria of first-price auctions with correlated values. Although some equilibrium computation methods exist for auctions with independent values, the correlation of bidders' values introduces significant complications that render the existing methods unsatisfactory. Our empirical contribution is a step towards filling this gap. We report surprisingly good numerical convergence of Fictitious Play toward an $\varepsilon$-equilibrium for an extensive set of instances. By doing so, we extend the insights of [39] to the correlated setting. These preliminary results call for further investigations into the properties of fictitious play algorithms on first-price auctions. 1. since the context is clear, we will use the term Nash equilibrium, or just equilibrium in this article

Problem

• first-price auctions
• correlated values
• Nash equilibria
• equilibrium computation

Innovation

• Fictitious Play
• first-price auctions
• correlated values
• Nash equilibrium
• empirical convergence