In non-truthful auctions, agents' utility for a strategy depends on the strategies of the opponents and also the prior distribution over their private types; the set of Bayes Nash equilibria generally has an intricate dependence on the prior. Using the First Price Auction as our main demonstrating example, we show that $\tilde O(n / \epsilon^2)$ samples from the prior with $n$ agents suffice for an algorithm to learn the interim utilities for all monotone bidding strategies. As a consequence, this number of samples suffice for learning all approximate equilibria. We give almost matching (up to polylog factors) lower bound on the sample complexity for learning utilities. We also consider a setting where agents must pay a search cost to discover their own types. Drawing on a connection between this setting and the first price auction, discovered recently by Kleinberg et al. (2016), we show that $\tilde O(n / \epsilon^2)$ samples suffice for utilities and equilibria to be estimated in a near welfare-optimal descending auction in this setting. En route, we improve the sample complexity bound, recently obtained by Guo et al. (2020), for the Pandora's Box problem, which is a classical model for sequential consumer search.

中文翻译：

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在非真实拍卖中学习效用和均衡

在非真实拍卖中，代理人对策略的效用取决于对手的策略以及他们私人类型的先验分布；贝叶斯纳什均衡集通常对先验具有复杂的依赖性。使用 First Price Auction 作为我们的主要演示示例，我们展示了 $\tilde O(n / \epsilon^2)$ 来自具有 $n$ 代理的先验样本足以让算法学习所有单调投标策略的临时效用. 因此，这个样本数量足以学习所有近似均衡。我们给出了学习效用的样本复杂度的几乎匹配（最多可达多对数因子）下限。我们还考虑了一种设置，即代理必须支付搜索成本才能发现自己的类型。利用此设置与首价拍卖之间的联系，最近由 Kleinberg 等人发现。（2016 年），我们表明 $\tilde O(n / \epsilon^2)$ 样本足以在这种情况下在接近福利最优的降序拍卖中估计效用和均衡。在此过程中，我们改进了郭等人最近获得的样本复杂度界限。（2020），针对潘多拉魔盒问题，这是顺序消费者搜索的经典模型。