In online advertising, automated bidding (auto-bidding) has become a widely-used tool for advertisers to automatically make bids on different impressions in real time. Instead of submitting bids for each single impression, advertisers in auto-bidding submit their high-level objectives and constraints to the auto-bidding tool, and observe the cumulative advertising performances after all the auctions within a time period have been finished. Motivated by the features of automated bidding, we aim to design auctions with private financial constraints for value-maximizing bidders. Specifically, we consider budget and ROI, the two most common financial constraints in online advertising, as the private information of advertisers, and analyse the conditions of truthfulness. We show that every non-decreasing function with budget as input could be mapped to a truthful auction mechanism with budget and ROI as input, but this mapping procedure also introduces complex value grouping structures into mechanism design. To achieve feasible and implementable auctions, we design a truthful auto-bidding auction mechanism with adjustable rank score functions. As the key design to guarantee truthfulness, our auction utilizes the bidder's budget constraint to compute a critical ROI, which enables comparisons between the budget and ROI constraint. We conduct experiments under different auto-bidding settings to validate the performance of our proposed auction in terms of revenue and social welfare.

翻译：在在线广告中，自动竞价已成为广告主实时自动对不同曝光进行出价的广泛采用工具。自动竞价模式下，广告主无需对每次曝光逐一提交出价，而是将高层目标和约束提交至自动竞价工具，并在时段内所有拍卖结束后观察累积广告效果。受自动竞价特性启发，我们旨在为价值最大化投标者设计具有私有财务约束的拍卖机制。具体而言，我们将预算和投资回报率（广告中最常见的两种财务约束）视为广告主的私有信息，并分析了真实性的条件。我们证明，任何以预算为输入的非递减函数均可映射为以预算和投资回报率为输入的真实拍卖机制，但该映射过程会在机制设计中引入复杂的价值分组结构。为设计可行且可实施的拍卖，我们提出了一种具有可调排名得分函数的真实自动竞价拍卖机制。作为保证真实性的关键设计，本拍卖利用投标者的预算约束计算临界投资回报率，从而实现预算与投资回报率约束的比较。我们在不同自动竞价设置下进行实验，验证了所提拍卖在收入和社福效益方面的性能。