An empirical study of Fictitious Play for estimating Nash equilibria in first-price auctions with correlated values
2026-06-15 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors study how to find Nash equilibria in first-price auctions when bidders' values are related or correlated, which is more complex than when values are independent. They show that using a method called Fictitious Play works surprisingly well to approximate these equilibria in many cases. This extends previous work done for independent values to the correlated setting. Their findings suggest that more research on Fictitious Play in these auctions is needed.
Nash equilibriumFirst-price auctionCorrelated valuesFictitious PlayEquilibrium computationGame theoryAuction theoryNumerical convergence
Authors
Benjamin Heymann, Panayotis Mertikopoulos
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