Approximating Gains-from-Trade in Matching Markets

TL;DR

This paper introduces a simple randomized truthful mechanism for two-sided matching markets with complex constraints, achieving a constant-factor approximation to the maximum expected gains-from-trade, thus advancing mechanism design in general settings.

Contribution

It extends prior work by providing the first constant-factor approximation mechanism for general two-sided matching markets with downward-closed constraints.

Findings

The mechanism guarantees a constant-factor approximation to optimal GFT.

It resolves an open problem from Cai et al. (2021).

The approach applies to more general market settings than previous models.

Abstract

A central challenge in mechanism design is to develop truthful trade mechanisms that maximize the expected gains-from-trade (GFT) in two-sided markets with strategic agents. As achieving the full GFT is generally impossible, much of the literature has focused on constant-factor approximations. Existing results, however, are limited to the highly structured settings of bilateral trade and double auctions, in which every buyer can trade with every seller. We consider the significantly more general setting of two-sided matching markets with arbitrary downward-closed constraints on the family of allowed matchings. For this setting, we present a simple randomized truthful mechanism that guarantees a constant-factor approximation to the optimal expected GFT. This result also resolves an open problem posed by Cai, Goldner, Ma, and Zhao (2021).