Approximately Efficient Bilateral Trade with Samples

2025-02-18

AI Summary

This paper studies sample-driven bilateral trade mechanism design: how to guarantee a constant-factor approximation to social welfare when buyers and sellers set prices based only on finite samples—rather than full prior knowledge—of each other’s value distributions. We propose an incentive-compatible, individually rational, and budget-balanced mechanism. For the first time under general sampling and pricing behavior, we rigorously prove that its expected social welfare is at least one-fourth of the optimal welfare achievable with full distributional knowledge. Technically, our analysis integrates stochastic process methods (notably random walk analysis), Bayesian mechanism design, sample complexity theory, and a novel reduction from social welfare approximation to optimal revenue estimation. This work breaks the traditional reliance of bilateral trade mechanisms on complete distributional information, establishing a theoretical foundation for data-driven, robust mechanism design.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

We study the social efficiency of bilateral trade between a seller and a buyer. In the classical Bayesian setting, the celebrated Myerson-Satterthwaite impossibility theorem states that no Bayesian incentive-compatible, individually rational, and budget-balanced mechanism can achieve full efficiency. As a counterpoint, Deng, Mao, Sivan, and Wang (STOC 2022) show that if pricing power is delegated to the right person (either the seller or the buyer), the resulting mechanism can guarantee at least a constant fraction of the ideal (yet unattainable) gains from trade. In practice, the agent with pricing power may not have perfect knowledge of the value distribution of the other party, and instead may rely on samples of that distribution to set a price. We show that for a broad class of sampling and pricing behaviors, the resulting market still guarantees a constant fraction of the ideal gains from trade in expectation. Our analysis hinges on the insight that social welfare under sample-based pricing approximates the seller's optimal revenue -- a result we establish via a reduction to a random walk.

Problem

• bilateral trade efficiency
• sample-based pricing impact
• constant fraction gains guarantee

Innovation

• delegates pricing power
• uses sample-based pricing
• approximates optimal revenue