On the Efficiency of Fair and Truthful Trade Mechanisms

2025-02-26

AI Summary

This paper investigates the trade-off between fairness and social efficiency in Bayesian bilateral trade, where conventional fairness notions (e.g., equality of outcomes) often degrade social welfare under private information. To address this, the authors introduce *KS-fairness*—a novel fairness criterion requiring equal ex-ante shares of each party’s ideal utility—and design a simple mechanism satisfying both incentive compatibility and KS-fairness. Theoretically, the mechanism guarantees at least 50% of the optimal expected revenue under general value distributions, and this approximation ratio is tight. Under refined assumptions—specifically, when the seller’s value is zero and the buyer’s value distribution satisfies regularity or the monotone hazard rate (MHR) condition—the mechanism surpasses the 1/2 barrier, yielding tight upper and lower bounds. Integrating tools from Bayesian mechanism design, optimal auction theory, and probabilistic analysis, this work establishes a new paradigm for fair mechanism design that jointly ensures efficiency and implementability.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Social Networks and Social Media: Fairness and bias in social network and social media analysis

Abstract

We consider the impact of fairness requirements on the social efficiency of truthful mechanisms for trade, focusing on Bayesian bilateral-trade settings. Unlike the full information case in which all gains-from-trade can be realized and equally split between the two parties, in the private information setting, equitability has devastating welfare implications (even if only required to hold ex-ante). We thus search for an alternative fairness notion and suggest requiring the mechanism to be KS-fair: it must ex-ante equalize the fraction of the ideal utilities of the two traders. We show that there is always a KS-fair (simple) truthful mechanism with expected gains-from-trade that are half the optimum, but always ensuring any better fraction is impossible (even when the seller value is zero). We then restrict our attention to trade settings with a zero-value seller and a buyer with value distribution that is Regular or MHR, proving that much better fractions can be obtained under these conditions.

Problem

• Impact of fairness on trade efficiency
• KS-fair mechanism for equitable utilities
• Improved trade fractions with zero-value seller

Innovation

• KS-fair truthful mechanism
• equalizes ideal utilities
• optimizes trade efficiency