Improved Approximation to First-Best Gains-from-Trade

TL;DR

This paper improves the approximation ratio for bilateral trade mechanisms, showing that a new mechanism achieves at least a 1/3.15 approximation of the optimal gains-from-trade, advancing understanding of trade efficiency under incentive constraints.

Contribution

The paper presents an improved lower bound of 1/3.15 for the approximation ratio of a trade mechanism, surpassing previous bounds, and analyzes the seller-pricing mechanism under specific distribution assumptions.

Findings

Improved the approximation ratio from 1/8.23 to 1/3.15.

Determined the exact worst-case ratio for seller-pricing under monotone hazard rate.

Provided insights into mechanism efficiency in bilateral trade scenarios.

Abstract

We study the two-agent single-item bilateral trade. Ideally, the trade should happen whenever the buyer's value for the item exceeds the seller's cost. However, the classical result of Myerson and Satterthwaite showed that no mechanism can achieve this without violating one of the Bayesian incentive compatibility, individual rationality and weakly balanced budget conditions. This motivates the study of approximating the trade-whenever-socially-beneficial mechanism, in terms of the expected gains-from-trade. Recently, Deng, Mao, Sivan, and Wang showed that the random-offerer mechanism achieves at least a 1/8.23 approximation. We improve this lower bound to 1/3.15 in this paper. We also determine the exact worst-case approximation ratio of the seller-pricing mechanism assuming the distribution of the buyer's value satisfies the monotone hazard rate property.