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

翻译：本研究关注相关价值第一价格拍卖中纳什均衡的计算问题。尽管针对独立价值拍卖已存在若干均衡计算方法，但竞标者价值的相关性带来了显著复杂性，使得现有方法难以令人满意。我们的实证贡献在于向填补这一空白迈出了关键一步。我们报告了虚构博弈（Fictitious Play）在大量实例中令人惊讶的良好数值收敛性，能够逼近ε-均衡。通过这一工作，我们将文献[39]的洞见拓展至相关价值情境。这些初步研究结果呼吁进一步探究虚构博弈算法在第一价格拍卖中的性质。注：由于研究背景明确，本文中将使用"纳什均衡"或简称"均衡"指代该概念。