Incentive Compatibility in the Auto-bidding World

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.