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

TL;DR

This paper characterizes the Pareto frontier of truthful auction mechanisms in Bayesian settings, analyzes fairness and efficiency tradeoffs using bargaining solutions, and compares their performance under different distributional assumptions.

Contribution

It provides a complete structural characterization of Pareto-optimal mechanisms and evaluates fairness solutions like Kalai-Smorodinsky and Nash in large markets.

Findings

Pareto frontier characterized under natural assumptions

Kalai-Smorodinsky solution yields near-optimal welfare in large markets

Performance of fairness solutions varies significantly with distributional assumptions

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.