Mechanism Design via Market Clearing-Prices for Value Maximizers under Budget and RoS Constraints

2026-02-22

AI Summary

This work addresses value-maximizing buyers in online advertising who face private budget constraints and private return-on-spend (RoS) constraints. It is the first to incorporate RoS constraints into an extended Eisenberg–Gale convex optimization framework to characterize market equilibrium, and leverages this characterization to design an incentive-compatible and revenue-efficient market-clearing mechanism. The proposed mechanism achieves a tight 1/2-approximation of the optimal revenue attainable by any feasible mechanism. Furthermore, the authors develop a decentralized online learning algorithm that converges to equilibrium utilities and revenue with sublinear regret of order Õ(√m) over m auction rounds. By integrating mechanism design, market equilibrium theory, and online learning, this work provides both theoretical guarantees and practical solutions for automated bidding under financial constraints.

Technology Category

• Multiagent Systems: Mechanism Design
• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising

Abstract

The transition to auto-bidding in online advertising has shifted the focus of auction theory from quasi-linear utility maximization to value maximization subject to financial constraints. We study mechanism design for buyers with private budgets and private Return-on-Spend (RoS) constraints, but public valuations, a setting motivated by modern advertising platforms where valuations are predicted via machine learning models. We introduce the extended Eisenberg-Gale program, a convex optimization framework generalized to incorporate RoS constraints. We demonstrate that the solution to this program is unique and characterizes the market's competitive equilibrium. Based on this theoretical analysis, we design a market-clearing mechanism and prove two key properties: (1) it is incentive-compatible with respect to financial constraints, making truthful reporting the optimal strategy; and (2) it achieves a tight 1/2-approximation of the first-best revenue benchmark, the maximum revenue of any feasible mechanism, regardless of IC. Finally, to enable practical implementation, we present a decentralized online algorithm. Ignoring logarithmic factors, we prove that under this algorithm, both the seller's revenue and each buyer's utility converge to the equilibrium benchmarks with a sublinear regret of $\tilde{O}(\sqrt{m})$ over $m$ auctions.

Problem

• mechanism design
• value maximization
• budget constraints
• Return-on-Spend constraints
• market clearing

Innovation

• mechanism design
• market clearing
• Return-on-Spend constraints
• Eisenberg-Gale program
• incentive compatibility