Welfare Maximization in Bilateral Trade: Improved Approximation Guarantees Beyond the Fixed Price Barrier

2026-06-03

AI Summary

This work addresses the long-standing limitation in bilateral trade mechanisms, where fixed-price rules are known to achieve at most a 0.7381 approximation of optimal social welfare. Challenging this theoretical barrier, the paper introduces a novel buyer-offer mechanism with a seller-specified reserve price: the buyer submits a single offer no lower than the reserve, and the seller, following a dominant strategy, decides whether to accept it. By integrating mechanism design theory with probabilistic analysis, the authors optimize the choice of the reserve price and construct—for the first time—a non-fixed-price mechanism that guarantees at least 0.746 times the optimal social welfare. This result refutes the presumed optimality of fixed-price mechanisms and establishes a new benchmark for incentive-compatible welfare guarantees in bilateral trade.

Abstract

We study the setting of welfare maximization in bilateral trade, where the values of both the buyer and the seller are drawn from independent distributions. Our goal is to maximize social welfare. In this setting, fixed price mechanisms have been extensively studied. In a fixed price mechanism, there is a price $p$ that depends only on the distributions of the buyer and the seller. Trade occurs if and only if the buyer's value is at least $p$ and the seller's value is at most $p$. A long line of work has culminated in determining almost exactly the approximation ratios achievable by fixed price mechanisms: there exists a fixed price mechanism that obtains at least a $0.72$ fraction of the social welfare, but no fixed price mechanism can guarantee more than a $0.7381$ fraction of it [Cai and Wu, STOC'23; Liu, Ren, and Wang, STOC'23]. No other incentive-compatible mechanism is known to beat the performance of fixed-price mechanisms in this setting. This paper shows how to achieve a larger fraction of the optimal welfare with other classes of mechanisms. Specifically, we study the buyer-offering mechanism with a reserve price. In this mechanism, the buyer observes its value and makes a take-it-or-leave-it offer to the seller, where the offer is at least the reserve price. Beyond its simplicity, this natural mechanism is attractive because the seller always has a dominant strategy: accept the offer if its value is at most the offer, and otherwise reject it. We show that there always exists a reserve price that guarantees a $0.746$ fraction of the social welfare. This not only improves upon the best previously known approximation guarantee for the problem, but also demonstrates that fixed-price mechanisms are not optimal in this setting.

Problem

• bilateral trade
• welfare maximization
• fixed price mechanism
• approximation guarantee
• incentive compatibility

Innovation

• bilateral trade
• welfare maximization
• buyer-offering mechanism
• reserve price
• approximation guarantee