Subquadratic Subsidies for Nonnegative or Nonpositive Valuations

2026-09-08

AI Summary

研究通过提供总额为O(n^1.5√log n)的补贴，在非负或非正值评估下实现n个参与者间的无嫉妒公平分配问题。

Abstract

We study envy-freeness with subsidies for indivisible items beyond additive valuations. Assuming that every single-item marginal value lies in $[-1,1]$, we prove that a total subsidy of $O(n^{3/2}\sqrt{\log n})$ suffices to achieve envy-freeness among $n$ agents whenever all agents assign nonnegative values to every bundle or all assign nonpositive values to every bundle. These valuation classes include monotone goods and monotone chores, respectively, but do not require monotonicity. Our result establishes the first subquadratic total-subsidy bound for general monotone valuations that holds for every number of agents.

Problem

• envy-freeness
• subsidies
• indivisible items
• nonnegative valuations
• nonpositive valuations

Innovation

• subquadratic subsidies
• nonnegative or nonpositive valuations
• envy-freeness