Advertisers in online ad auctions are increasingly using auto-bidding mechanisms to bid into auctions instead of directly bidding their value manually. One prominent auto-bidding format is the target cost-per-acquisition (tCPA) which maximizes the volume of conversions subject to a return-of-investment constraint. From an auction theoretic perspective however, this trend seems to go against foundational results that postulate that for profit-maximizing bidders, it is optimal to use a classic bidding system like marginal CPA (mCPA) bidding rather than using strategies like tCPA. In this paper we rationalize the adoption of such seemingly sub-optimal bidding within the canonical quasi-linear framework. The crux of the argument lies in the notion of commitment. We consider a multi-stage game where first the auctioneer declares the auction rules; then bidders select either the tCPA or mCPA bidding format and then, if the auctioneer lacks commitment, it can revisit the rules of the auction (e.g., may readjust reserve prices depending on the observed bids). Our main result is that so long as a bidder believes that the auctioneer lacks commitment to follow the rule of the declared auction then the bidder will make a higher profit by choosing the tCPA format over the mCPA format. We then explore the commitment consequences for the auctioneer. In a simplified version of the model where there is only one bidder, we show that the tCPA subgame admits a credible equilibrium while the mCPA format does not. That is, when the bidder chooses the tCPA format the auctioneer can credibly implement the auction rules announced at the beginning of the game. We also show that, under some mild conditions, the auctioneer's revenue is larger when the bidder uses the tCPA format rather than mCPA. We further quantify the value for the auctioneer to be able to commit to the declared auction rules.

翻译：在线广告拍卖中的广告主越来越多地使用自动竞价机制来参与拍卖，而非手动直接出价。其中一种突出的自动竞价形式是目标每次获取成本（tCPA），它在满足投资回报约束的前提下最大化转化量。然而，从拍卖理论的角度来看，这一趋势似乎与基础结论相悖：经典理论认为，追求利润最大化的竞标者应使用如边际每次获取成本（mCPA）竞价等经典竞价系统，而非tCPA这类策略。本文在标准拟线性框架下，为这种看似次优的竞价方式的采用提供了合理依据。论证的核心在于承诺的概念。我们考虑一个多阶段博弈：首先拍卖方宣布拍卖规则；然后竞标者选择tCPA或mCPA竞价格式；若拍卖方缺乏承诺能力，其可重新审视拍卖规则（例如，根据观察到的出价调整保留价）。我们的主要结论是：只要竞标者认为拍卖方缺乏遵循已宣布拍卖规则的承诺能力，选择tCPA格式将比mCPA格式获得更高利润。随后，我们探讨了拍卖方的承诺后果。在仅有一名竞标者的简化模型版本中，我们证明tCPA子博弈存在可信均衡，而mCPA格式则不然。即当竞标者选择tCPA格式时，拍卖方能够可信地执行博弈开始时宣布的拍卖规则。我们还证明，在温和条件下，竞标者使用tCPA格式时拍卖方的收益高于mCPA格式。我们进一步量化了拍卖方能够承诺遵守已宣布拍卖规则的价值。