In non-truthful auctions such as first-price and all-pay auctions, the independent strategic behaviors of bidders, with the corresponding Bayes-Nash equilibrium notion, are notoriously difficult to characterize and can cause undesirable outcomes. An alternative approach to achieve better outcomes in non-truthful auctions is to coordinate the bidders: let a mediator make incentive-compatible recommendations of correlated bidding strategies to the bidders, namely, implementing a Bayes correlated equilibrium (BCE). The implementation of BCE, however, requires knowledge of the distributions of bidders' private valuations, which is often unavailable. We initiate the study of the sample complexity of learning Bayes correlated equilibria in non-truthful auctions. We prove that the set of strategic-form BCEs in a large class of non-truthful auctions, including first-price and all-pay auctions, can be learned with a polynomial number $\tilde O(\frac{n}{\varepsilon^2})$ of samples of bidders' values. This moderate number of samples demonstrates the statistical feasibility of learning to coordinate bidders. Our technique is a reduction to the problem of estimating bidders' expected utility from samples, combined with an analysis of the pseudo-dimension of the class of all monotone bidding strategies.

翻译：在诸如首价拍卖和全付拍卖等非真实拍卖中，投标人独立的策略行为及其对应的贝叶斯-纳什均衡概念，因其难以刻画且可能导致不良结果而臭名昭著。在非真实拍卖中实现更好结果的一种替代方法是协调投标人：让一个中介机构向投标人做出激励相容的、相关的投标策略推荐，即实现贝叶斯相关均衡。然而，贝叶斯相关均衡的实现需要知道投标人私人估值的分布，而这通常是未知的。我们首次研究了在非真实拍卖中学习贝叶斯相关均衡的样本复杂度。我们证明，在一大类非真实拍卖（包括首价拍卖和全付拍卖）中，其策略形式的贝叶斯相关均衡集合可以通过 $\tilde O(\frac{n}{\varepsilon^2})$ 个投标人估值的样本进行学习。这个适中的样本数量证明了学习协调投标人在统计上是可行的。我们的技术是将问题归约为从样本中估计投标人期望效用的问题，并结合对所有单调投标策略类的伪维度分析。