Asymptotic Max-Min Fair Allocation with Random Utilities

2026-09-16

AI Summary

研究了在随机效用下不可分割商品的最大最小公平分配的渐近行为，通过分布分位数描述最大最小值，并证明了对于轻尾分布，随着市场扩大，相对效率损失趋于零。

Abstract

We investigate the asymptotic behavior of max-min fair allocations for indivisible goods under i.i.d. random utilities. For $N$ agents and $K$ goods with utilities ${\mU_{i,j}}$ drawn independently from a common distribution $F$, we derive asymptotic characterizations of the max-min value in the balanced case $K=N$ (and in $K=LN$ extensions) via distributional quantiles. We then study the efficiency impact of max-min fairness by comparing the resulting total welfare with the optimal sum welfare. For distributions with sufficiently light tails, we prove that the relative efficiency loss converges to zero as the market grows, implying that max-min fairness incurs negligible welfare loss in large random instances for a broad class of distributions.

Problem

• max-min fair allocation
• indivisible goods
• random utilities
• asymptotic behavior
• welfare efficiency

Innovation

• asymptotic behavior
• max-min fair allocation
• random utilities
• distributional quantiles
• efficiency impact