Whoever Said Money Won't Solve All Your Problems? Weighted Envy-free Allocation with Subsidy

TL;DR

This paper develops polynomial-time algorithms for fair allocation of indivisible items among agents with weights, achieving weighted-envy-freeness with bounded subsidies, and introduces new methods for cases with insufficient budgets.

Contribution

It introduces the first polynomial-time algorithms for weighted-envy-freeness with subsidies and addresses allocations with limited budgets, extending fairness concepts to weighted settings.

Findings

Algorithms guarantee bounded subsidies for monotone valuations.

Efficient method for allocating items and money with insufficient budget.

New approach applicable even in unweighted scenarios.

Abstract

We explore solutions for fairly allocating indivisible items among agents assigned weights representing their entitlements. Our fairness goal is weighted-envy-freeness (WEF), where each agent deems their allocated portion relative to their entitlement at least as favorable as any others relative to their own. Often, achieving WEF necessitates monetary transfers, which can be modeled as third-party subsidies. The goal is to attain WEF with bounded subsidies. Previous work relied on characterizations of unweighted envy-freeness (EF), that fail in the weighted setting. This makes our new setting challenging. We present polynomial-time algorithms that compute WEF allocations with a guaranteed upper bound on total subsidy for monotone valuations and various subclasses thereof. We also present an efficient algorithm to compute a fair allocation of items and money, when the budget is not enough to make the allocation WEF. This algorithm is new even for the unweighted setting.