We study the complexity of computing Bayes-Nash equilibria in single-item first-price auctions. We present the first efficient algorithms for the problem, when the bidders' values for the item are independently drawn from the same continuous distribution, under both established variants of continuous and finite bidding sets. More precisely, we design polynomial-time algorithms for the white-box model, where the distribution is provided directly as part of the input, and query-efficient algorithms for the black-box model, where the distribution is accessed via oracle calls. Our results settle the computational complexity of the problem for bidders with i.i.d. values.

翻译：我们研究了单物品一级价格拍卖中贝叶斯-纳什均衡的计算复杂性。当竞拍者对物品的估值独立同分布于同一连续分布时，我们提出了该问题的首批高效算法，涵盖连续出价集与有限出价集两种既定变体。具体而言，我们为白盒模型设计了多项式时间算法（该模型下分布直接作为输入的一部分提供），并为黑盒模型设计了查询高效算法（该模型下分布通过预言机调用访问）。我们的研究成果解决了竞拍者估值独立同分布时该问题的计算复杂性。