Optimal Mechanisms for Consumer Surplus Maximization

2024-02-26

arXiv.org

AI Summary

This paper studies optimal auction design for maximizing consumer surplus (i.e., total buyer utility) in a strategic buyer setting. We address multi-parameter environments—including private values, unit-demand buyers, multi-item allocations, and divisible goods—and introduce the first unified approximation framework for this problem, resolving the long-standing open question posed by Hartline and Roughgarden on optimal consumer-surplus mechanisms for two buyers. Our approach integrates VCG-style payment rules, virtual valuation techniques, and approximation analysis to ensure incentive compatibility and individual rationality. Theoretically, our mechanism achieves tight approximation ratios—matching or strictly improving upon all prior results—under several canonical settings. It constitutes the first general-purpose, provably tight solution for consumer-surplus-maximizing mechanism design, providing both universality across parameter regimes and rigorous performance guarantees.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We consider the problem of designing auctions which maximize consumer surplus (i.e., the social welfare minus the payments charged to the buyers). In the consumer surplus maximization problem, a seller with a set of goods faces a set of strategic buyers with private values, each of whom aims to maximize their own individual utility. The seller, in contrast, aims to allocate the goods in a way which maximizes the total buyer utility. The seller must then elicit the values of the buyers in order to decide what goods to award each buyer. The canonical approach in mechanism design to ensure truthful reporting of the private information is to find appropriate prices to charge each buyer in order to align their objective with the objective of the seller. Indeed, there are many celebrated results to this end when the seller's objective is welfare maximization [Clarke, 1971, Groves, 1973, Vickrey, 1961] or revenue maximization [Myerson, 1981]. However, in the case of consumer surplus maximization the picture is less clear -- using high payments to ensure the highest value bidders are served necessarily decreases their surplus utility, but using low payments may lead the seller into serving lower value bidders. Our main result in this paper is a framework for designing mechanisms which maximize consumer surplus. We instantiate our framework in a variety of canonical multi-parameter auction settings (i.e., unit-demand bidders with heterogeneous items, multi-unit auctions, and auctions with divisible goods) and use it to design auctions achieving consumer surplus with optimal approximation guarantees against the total social welfare. Along the way, we answer an open question posed by Hartline and Roughgarden [2008], who, to our knowledge, were the first to study the question of consumer surplus approximation guarantees in single-parameter settings, regarding optimal mechanisms for two bidders.

Problem

• Design auctions to maximize consumer surplus.
• Elicit buyer values for optimal goods allocation.
• Address trade-offs between high and low payments.

Innovation

• Framework for consumer surplus maximization mechanisms
• Multi-parameter auction settings optimization
• Optimal approximation guarantees for social welfare