Revenue Guarantee of Anonymous Pricing for Mixed Bidders:Bridging Value and Utility Maximizers
2026-06-29 • Computer Science and Game Theory
Computer Science and Game Theory
AI summaryⓘ
The authors study a market where buyers have two different ways of deciding what to pay: some aim to maximize their overall happiness (utility maximizers), while others try to get the best value for the money they spend (value maximizers). They look at how a simple pricing method called Anonymous Pricing performs in such mixed settings. They prove that this pricing method can earn at least about 37% of the best possible revenue, which is better than previous results for just value maximizers. They also find that having more competition doesn’t always mean more money when value maximizers are involved, especially compared to auctions with similar pricing.
Mechanism DesignRevenue OptimizationValue MaximizersUtility MaximizersAnonymous PricingReturn-on-SpendFirst-Price AuctionHeterogeneous MarketsBehavioral Equivalence
Authors
Zhile Jiang, Stratis Skoulakis
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.