Efficient Two-Sided Markets with Limited Information
Paul Dütting, Federico Fusco, Philip Lazos, Stefano Leonardi, Rebecca Reiffenhäuser
TL;DR
This work investigates two-sided market design under private information and shows that, contrary to the traditional need for full priors, a single seller sample suffices to achieve near-optimal welfare in broad settings. It establishes an information-theoretic barrier against prior-free welfare approximation, and then develops computationally efficient single-sample mechanisms and black-box reductions that convert any one-sided truthful mechanism into a two-sided mechanism with only a constant-factor loss. Central contributions include the adjusted VCG mechanism achieving a 2-approximation for subadditive buyers, the Surplus Mechanism delivering a max{2α,3}-approximation for XOS buyers, and a Reserve Rehearsal scheme for double auctions that attains a 1+3.73α-approximation, all while preserving IR, DSIC, and BB/SBB properties. These results demonstrate that minimal prior information can yield robust, practical mechanisms often matching or surpassing prior-information-based approaches, with broad implications for design of efficient and fair two-sided marketplaces.
Abstract
A celebrated impossibility result by Myerson and Satterthwaite (1983) shows that any truthful mechanism for two-sided markets that maximizes social welfare must run a deficit, resulting in a necessity to relax welfare efficiency and the use of approximation mechanisms. Such mechanisms in general make extensive use of the Bayesian priors. In this work, we investigate a question of increasing theoretical and practical importance: how much prior information is required to design mechanisms with near-optimal approximations? Our first contribution is a more general impossibility result stating that no meaningful approximation is possible without any prior information, expanding the famous impossibility result of Myerson and Satterthwaite. Our second contribution is that one {\em single sample} (one number per item), arguably a minimum-possible amount of prior information, from each seller distribution is sufficient for a large class of two-sided markets. We prove matching upper and lower bounds on the best approximation that can be obtained with one single sample for subadditive buyers and additive sellers, regardless of computational considerations. Our third contribution is the design of computationally efficient blackbox reductions that turn any one-sided mechanism into a two-sided mechanism with a small loss in the approximation, while using only one single sample from each seller. On the way, our blackbox-type mechanisms deliver several interesting positive results in their own right, often beating even the state of the art that uses full prior information.