Fair Division of Chores with Budget Constraints

TL;DR

This paper introduces a budget-constrained model for fairly dividing indivisible chores among agents, establishing existence results and efficient algorithms for various fairness criteria.

Contribution

It systematically explores fair division of chores with budget constraints, proving existence of EFX allocations and providing polynomial-time algorithms for EF2 and EF1 allocations.

Findings

EFX allocations exist under the model.

EF2 allocations are computable in polynomial time.

Efficient algorithms are developed for divisible chores.

Abstract

We study fair allocation of indivisible chores to agents under budget constraints, where each chore has an objective size and disutility. This model captures scenarios where a set of chores need to be divided among agents with limited time, and each chore has a specific time needed for completion. We propose a budget-constrained model for allocating indivisible chores, and systematically explore the differences between goods and chores in this setting. We establish the existence of an EFX allocation. We then show that EF2 allocations are polynomial-time computable in general; for many restricted settings, we strengthen this result to EF1. For divisible chores, we develop an efficient algorithm for computing an EF allocation.