Multi-Parameter Mechanisms for Consumer Surplus Maximization
Tomer Ezra, Daniel Schoepflin, Ariel Shaulker
TL;DR
This paper addresses maximizing residual consumer surplus in auctions with private valuations by introducing a VCG-with-copies framework that augments the item space, runs VCG on the augmented instance, and rounds to the original domain with payments scaled to preserve truthfulness. The framework enables prior-free mechanisms with provable guarantees across multiple multi-parameter settings, including unit-demand, multi-unit, and divisible goods, achieving $O(\log n)$-approximation to the first-best welfare and, in Bayesian regimes, improved $O(\log(1+\frac{nc}{m}))$ bounds under a no-superstar-item assumption. The results also resolve an open question for two bidders in the single-item case and connect to broader literature on money-burning, frugal design, and mechanism design without money. Collectively, the work advances understanding of how limited monetary transfers can still yield strong consumer-surplus performance in complex auction environments and suggests avenues for extending the framework to richer valuation classes and alternative benchmarks.
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] for the two bidders single item setting.