Risk-Averse and Optimistic Advertiser Incentive Compatibility in Auto-bidding

The rise of auto-bidding in online advertising has created new challenges for ensuring advertiser incentive compatibility, particularly when advertisers delegate bidding to agents with high-level constraints. One challenge in defining incentive compatibility is the multiplicity of equilibria. After advertisers submit their reports, it is unclear what the result will be and one only has knowledge of a range of possible results. Nevertheless, Alimohammadi et al. [4] proposed a notion of Auto-bidding Incentive Compatibility (AIC) which serves to highlight that standard auctions may not incentivize truthful reporting of these constraints. However, their definition of AIC is very stringent as it requires that the worst-case outcome of an advertiser's truthful report is at least as good as the best-case outcome of any of the advertiser's possible deviations. Indeed, they show that both First-Price Auction (FPA) and Second-Price Auction (SPA) are not AIC. Moreover, the AIC definition precludes having ordinal preferences on the possible constraints that the advertiser can report. In this paper, we introduce two refined and relaxed concepts: Risk-Averse Autobidding Incentive Compatibility (RAIC) and Optimistic Auto-bidding Incentive Compatibility (OAIC). RAIC (OAIC) stipulates that truthful reporting is preferred if its least (most) favorable equilibrium outcome is no worse than the least (most) favorable equilibrium outcome from any misreport. This distinction allows for a clearer modeling of ordinal preferences for advertisers with differing attitudes towards equilibrium uncertainty. We demonstrate that SPA satisfies both RAIC and OAIC. Furthermore, we show that SPA also meets these conditions for two advertisers when they are assumed to employ uniform bidding strategies. These findings provide new insights into the incentive properties of SPA in auto-bidding environments, particularly when considering advertisers' perspectives on equilibrium selection. From the auto-bidders' perspective, the primary objective is to identify optimal bidding strategies that maximize a specific goal while adhering to advertiser constraints [1, 7] . From the auction design standpoint, research can be categorized into several areas: the existence and computational complexity