Revenue Guarantee of Anonymous Pricing for Mixed Bidders:Bridging Value and Utility Maximizers

2026-06-29

AI Summary

This study addresses the theoretical and computational challenges of revenue-optimal mechanism design in heterogeneous markets comprising both value maximizers and utility maximizers. It extends, for the first time, the revenue guarantees of anonymous pricing from settings with only utility maximizers to environments with mixed bidders. By constructing a behavioral equivalence between the two bidder types under a uniform price and leveraging tools from mechanism design theory alongside worst-case approximation ratio analysis, the paper establishes that anonymous pricing achieves a $1/e$-approximation to the optimal revenue—improving upon the previously known bound of $1/(2(1 - 1/e))$ for pure utility-maximizing settings—and provides an upper bound of $1/2.62$. The work also uncovers a counterintuitive phenomenon: the presence of value maximizers can weaken competition and thereby reduce mechanism revenue.

Abstract

Mechanism design increasingly faces heterogeneous environments containing both traditional utility maximizers and value maximizers, the latter of whom seek to maximize acquired value subject to Return-on-Spend constraints. Designing revenue-optimal mechanisms for such multi-dimensional settings is both computationally and theoretically challenging. To address this complexity, we investigate the revenue guarantees of \textit{Anonymous Pricing} (AP), a simple and practical mechanism, in heterogeneous markets composed of both value and utility maximizers. By establishing a structural behavioral equivalence between value and utility maximizers, we show that AP, with an appropriately chosen price, achieves a \(1/e\) fraction of the optimal revenue. Our result improves upon the recent \( \frac{1}{2}(1 - 1/e) \) guarantee established by Deng et al.~(2022) for pure value maximizers, while extending it to mixed bidder types (both value and utility maximizers). We additionally establish an upper bound of \(1/2.62\) for AP. Finally, we demonstrate a counterintuitive phenomenon: competition can reduce revenue with the presence of value maximizers. In particular, running a First-Price Auction with the exact same reserve price as AP can, in the presence of value maximizers, generate lower revenue than AP itself.

Problem

• anonymous pricing
• value maximizers
• utility maximizers
• revenue guarantee
• heterogeneous bidders

Innovation

• Anonymous Pricing
• Value Maximizers
• Utility Maximizers
• Revenue Guarantee
• Mechanism Design