A New Lower Bound for the Random Offerer Mechanism in Bilateral Trade using AI-Guided Evolutionary Search
2026-03-09 • Machine Learning
Machine LearningArtificial IntelligenceComputer Science and Game Theory
AI summaryⓘ
The authors study a famous problem in economics about how well certain trade methods work when trying to be fair and efficient at the same time. They focus on a simple method called the Random-Offerer mechanism, which sometimes performs worse than the ideal but very complex solution. Using an AI-based search technique, the authors found new examples showing this simple method can be even less efficient than previously thought, widening the known gap between it and the best possible outcome. Their work improves understanding of the limits of simple trade mechanisms.
Myerson-Satterthwaite theorembilateral tradeBayesian incentive compatibilitybudget balancegains from tradeRandom-Offerer mechanismapproximation ratiovalue distributionsevolutionary searchmechanism design
Authors
Yang Cai, Vineet Gupta, Zun Li, Aranyak Mehta
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.