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

This study concerns the computation of the \textit{Nash equilibria} of \textit{first-price auctions} with \textit{correlated values}. Although some equilibrium computation methods exist for auctions with \textit{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 \textit{Fictitious Play} toward $\epsilon$-equilibrium for an extensive set of instances. By doing so, we extend the insights of Rabinovich 2013 to the correlated setting.