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

2025-08-22

AI Summary

Traditional advertiser-incentive-compatibility (AIC) definitions in automated bidding are overly restrictive, as they ignore advertisers’ ordinal preferences over multiple equilibria—such as risk aversion or optimism—when delegating bidding to agents. Method: We propose two relaxed incentive-compatibility notions—risk-averse IC and optimistic IC—that formally capture advertisers’ preferences over equilibrium outcome intervals. Using game-theoretic analysis and mechanism design, we characterize constrained delegated equilibria under first-price and second-price auctions. Results: We prove that the second-price auction satisfies both relaxed IC definitions, even under the standard two-advertiser uniform-value-distribution assumption; in contrast, the first-price auction fails to satisfy either. This work establishes a more behaviorally grounded theoretical foundation for automated bidding mechanisms and introduces a novel analytical framework that accommodates heterogeneous advertiser attitudes toward equilibrium multiplicity.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Adversarial Search

Application Category

• Economics, Online Markets and Human Computation: Advertising auctions, pricing, markets, and exchanges
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

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.

Problem

• Defining advertiser incentive compatibility in auto-bidding with multiple equilibria
• Relaxing stringent AIC requirements to accommodate ordinal preference modeling
• Analyzing Second-Price Auction's compliance with risk-averse and optimistic incentive compatibility

Innovation

• Risk-Averse Auto-bidding Incentive Compatibility (RAIC)
• Optimistic Auto-bidding Incentive Compatibility (OAIC)
• Second-Price Auction satisfies both RAIC and OAIC