Auto-bidding has recently become a popular feature in ad auctions. This feature enables advertisers to simply provide high-level constraints and goals to an automated agent, which optimizes their auction bids on their behalf. In this paper, we examine the effect of different auctions on the incentives of advertisers to report their constraints to the auto-bidder intermediaries. More precisely, we study whether canonical auctions such as first price auction (FPA) and second price auction (SPA) are auto-bidding incentive compatible (AIC): whether an advertiser can gain by misreporting their constraints to the autobidder. We consider value-maximizing advertisers in two important settings: when they have a budget constraint and when they have a target cost-per-acquisition constraint. The main result of our work is that for both settings, FPA and SPA are not AIC. This contrasts with FPA being AIC when auto-bidders are constrained to bid using a (sub-optimal) uniform bidding policy. We further extend our main result and show that any (possibly randomized) auction that is truthful (in the classic profit-maximizing sense), scalar invariant and symmetric is not AIC. Finally, to complement our findings, we provide sufficient market conditions for FPA and SPA to become AIC for two advertisers. These conditions require advertisers' valuations to be well-aligned. This suggests that when the competition is intense for all queries, advertisers have less incentive to misreport their constraints. From a methodological standpoint, we develop a novel continuous model of queries. This model provides tractability to study equilibrium with auto-bidders, which contrasts with the standard discrete query model, which is known to be hard. Through the analysis of this model, we uncover a surprising result: in auto-bidding with two advertisers, FPA and SPA are auction equivalent.

翻译：自动出价已成为广告拍卖中的一项流行功能。该功能允许广告商向自动代理提供高级约束和目标，由代理代其优化出价。本文研究了不同拍卖对广告商向自动出价中介报告其约束的激励影响。更准确地说，我们探讨了经典拍卖（如一级价格拍卖和二级价格拍卖）是否具有自动出价激励相容性，即广告商是否可以通过向自动出价器错误报告其约束而获利。我们考虑了两种重要场景下的价值最大化广告商：当它们具有预算约束时，以及当它们具有目标每次收购成本约束时。我们的主要结论是，在这两种场景下，一级和二级价格拍卖均不具有自动出价激励相容性。这与当自动出价者受限于使用（次优的）统一出价策略时一级价格拍卖具有自动出价激励相容性形成对比。我们进一步扩展了主要结论，表明任何（可能随机化的）拍卖，若其在经典利润最大化意义上是真实的、标量不变且对称的，则不具有自动出价激励相容性。最后，为了补充我们的发现，我们为一组两个广告商提供了使一级和二级价格拍卖成为自动出价激励相容的充分市场条件。这些条件要求广告商的估值高度一致。这表明当所有查询的竞争激烈时，广告商错误报告其约束的激励较小。从方法论角度来看，我们开发了一种新颖的查询连续模型。该模型为研究自动出价者的均衡提供了可处理性，这与已知难以处理的标准离散查询模型形成对比。通过分析该模型，我们发现了一个令人惊讶的结果：在两个广告商的自动出价中，一级和二级价格拍卖在拍卖上是等价的。