Pareto-Efficient Multi-Buyer Mechanisms: Characterization, Fairness and Welfare

2026-02-12

AI Summary

This study investigates the Pareto-optimal trade-off between seller revenue and buyer surplus in Bayesian single-item auctions. By modeling mechanism design as a cooperative game between the seller and buyers, the work fully characterizes the structure of Pareto-optimal mechanisms under regular and anti-MHR (monotone hazard rate) distributions. It further compares the welfare performance of the Kalai-Smorodinsky (KS) and Nash bargaining solutions. The results show that, in large markets with regular anti-MHR distributions, both fairness-based solutions achieve near-socially optimal welfare. However, under worst-case MHR distributions, only the KS solution guarantees at least half of the optimal welfare, whereas the Nash solution’s performance can degrade arbitrarily, highlighting a stark difference in their robustness to distributional perturbations.

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

A truthful mechanism for a Bayesian single-item auction results with some ex-ante revenue for the seller, and some ex-ante total surplus for the buyers. We study the Pareto frontier of the set of seller-buyers ex-ante utilities, generated by all truthful mechanisms when buyers values are sampled independently and identically (i.i.d.). We first provide a complete structural characterization of the Pareto frontier under natural distributional assumptions. For example, when valuations are drawn i.i.d. from a distribution that is both regular and anti-MHR, every Pareto-optimal mechanism is a second-price auction with a reserve no larger than the monopoly reserve. Building on this, we interpret the problem of picking a mechanism as a two-sided bargaining game, and analyze two canonical Pareto-optimal solutions from cooperative bargaining theory: the Kalai-Smorodinsky (KS) solution, and the Nash solution. We prove that when values are drawn i.i.d. from a distribution that is both regular and anti-MHR, in large markets both solutions yield near-optimal welfare. In contrast, under worst-case MHR distributions, their performance diverges sharply: the KS solution guarantees one-half of the optimal welfare, while the Nash solution might only achieve an arbitrarily small fraction of it. These results highlight the sensitivity of fairness-efficiency tradeoffs to distributional structure, and affirm the KS solution as the more robust notion of fairness for asymmetric two-sided markets.

Problem

• Pareto efficiency
• multi-buyer auction
• fairness
• welfare
• Bayesian mechanism design

Innovation

• Pareto efficiency
• truthful mechanism
• Kalai-Smorodinsky solution
• auction design
• fairness-efficiency tradeoff