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

TL;DR

This paper introduces relaxed incentive compatibility concepts, RAIC and OAIC, for auto-bidding, demonstrating that standard second-price auctions satisfy these conditions under certain assumptions, thus improving understanding of advertiser incentives.

Contribution

The paper proposes two new incentive compatibility notions, RAIC and OAIC, which accommodate ordinal preferences and equilibrium uncertainty, and shows SPA satisfies these in auto-bidding.

Findings

SPA satisfies RAIC and OAIC.

SPA satisfies these conditions for two advertisers with uniform bidding.

Provides new insights into incentive properties of SPA in auto-bidding.

Abstract

The rise of auto-bidding has created 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 reports, it is unclear what the result will be and one only has knowledge of a range of possible results. Nevertheless, Alimohammadi et al. proposed a notion of Auto-bidding Incentive Compatibility (AIC) which serves to highlight that auctions may not incentivize truthful reporting of 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 both First-Price Auction and Second-Price Auction 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 Auto-bidding 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. These findings provide new insights into the incentive properties of SPA in auto-bidding environments, particularly when considering advertisers' perspectives on equilibrium selection.