A New Lower Bound for the Random Offerer Mechanism in Bilateral Trade using AI-Guided Evolutionary Search

2026-03-09

AI Summary

This study investigates the worst-case efficiency loss of the Random-Offer (RO) mechanism in bilateral trade under Bayesian incentive compatibility and budget balance, quantified as the lower bound on the ratio between its expected revenue and the first-best benchmark. To this end, the paper introduces AlphaEvolve—an AI-driven evolutionary search framework—into mechanism design theory for the first time. By integrating neural network guidance, evolutionary algorithms, and formal verification, AlphaEvolve automatically constructs extremal instances in high-dimensional valuation spaces, overcoming the limitations of manual constructions. This approach yields novel counterexample distributions that tighten the known approximation ratio lower bound for the RO mechanism from 2.02 to 2.0749, revealing a more severe efficiency loss than previously recognized.

Technology Category

• Multiagent Systems: Mechanism Design
• Game Theory and Economic Paradigms: Mechanism Design
• Search and Optimization: Evolutionary Computation

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web

Abstract

The celebrated Myerson--Satterthwaite theorem shows that in bilateral trade, no mechanism can be simultaneously fully efficient, Bayesian incentive compatible (BIC), and budget balanced (BB). This naturally raises the question of how closely the gains from trade (GFT) achievable by a BIC and BB mechanism can approximate the first-best (fully efficient) benchmark. The optimal BIC and BB mechanism is typically complex and highly distribution-dependent, making it difficult to characterize directly. Consequently, much of the literature analyzes simpler mechanisms such as the Random-Offerer (RO) mechanism and establishes constant-factor guarantees relative to the first-best GFT. An important open question concerns the worst-case performance of the RO mechanism relative to first-best (FB) efficiency. While it was originally hypothesized that the approximation ratio $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}}$ is bounded by $2$, recent work provided counterexamples to this conjecture: Cai et al. proved that the ratio can be strictly larger than $2$, and Babaioff et al. exhibited an explicit example with ratio approximately $2.02$. In this work, we employ AlphaEvolve, an AI-guided evolutionary search framework, to explore the space of value distributions. We identify a new worst-case instance that yields an improved lower bound of $\frac{\text{GFT}_{\text{FB}}}{\text{GFT}_{\text{RO}}} \ge \textbf{2.0749}$. This establishes a new lower bound on the worst-case performance of the Random-Offerer mechanism, demonstrating a wider efficiency gap than previously known.

Problem

• bilateral trade
• Random-Offerer mechanism
• gains from trade
• first-best efficiency
• approximation ratio

Innovation

• AI-guided evolutionary search
• Random-Offerer mechanism
• bilateral trade
• gains from trade
• mechanism design