Approximating Gains-from-Trade in Matching Markets

2026-03-31

AI Summary

This work addresses a long-standing open problem in mechanism design: how to construct a truthful mechanism that achieves a constant-factor approximation of the optimal expected gains from trade (GFT) in two-sided matching markets with strategic agents and arbitrary downward-closed feasibility constraints. The paper proposes a simple randomized truthful mechanism that, for the first time, extends constant-factor GFT approximation guarantees—previously attainable only in highly structured settings such as bilateral trade or double auctions—to general two-sided matching markets. By integrating techniques from mechanism design, randomized algorithms, and combinatorial optimization, the proposed mechanism simultaneously ensures truthfulness and approximation guarantees under broad matching constraints, thereby resolving an open question posed by Cai et al. (2021).

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).

Problem

• gains-from-trade
• two-sided matching markets
• truthful mechanism
• downward-closed constraints
• approximation

Innovation

• two-sided matching markets
• gains-from-trade
• truthful mechanism
• constant-factor approximation
• downward-closed constraints