Weighted Envy-free Allocation with Subsidy

TL;DR

This paper studies fair allocation of indivisible items with subsidies, focusing on agents with weighted entitlements, providing characterizations, algorithms, and bounds for achieving weighted envy-free allocations.

Contribution

It introduces new characterizations and algorithms for weighted envy-free allocations, addressing the complexities introduced by agent weights and subsidies.

Findings

Characterizations of weighted envy-freeability

Algorithms for testing and achieving envy-free allocations

Bounds on subsidies needed for envy-freeness

Abstract

We consider the problem of fair allocation of indivisible items with subsidies when agents have weighted entitlements. After highlighting several important differences from the unweighted case, we present several results concerning weighted envy-freeability including general characterizations, algorithms for achieving and testing weighted envy-freeability, lower and upper bounds of the amount of subsidies for envy-freeable allocations, and algorithms for achieving weighted envy-freeability along with other properties.