On the Existence of EFX (and Pareto-Optimal) Allocations for Binary Chores

TL;DR

This paper proves the existence and polynomial-time computability of EFX and Pareto-optimal allocations for binary chores among multiple agents, extending previous results limited to three agents, and explores more general cost functions.

Contribution

It demonstrates the existence of EFX and PO allocations for additive binary chores with multiple agents, and analyzes EFX existence under broader cost functions.

Findings

EFX and PO allocations exist for additive binary chores with multiple agents.

EFX allocations can be computed in polynomial time for these chores.

For more general cost functions, EFX may not be compatible with PO, but EF allocations can still be computed.

Abstract

We study the problem of allocating a group of indivisible chores among agents while each chore has a binary marginal. We focus on the fairness criteria of envy-freeness up to any item (EFX) and investigate the existence of EFX allocations. We show that when agents have additive binary cost functions, there exist EFX and Pareto-optimal (PO) allocations that can be computed in polynomial time. To the best of our knowledge, this is the first setting of a general number of agents that admits EFX and PO allocations, before which EFX and PO allocations have only been shown to exist for three bivalued agents. We further consider more general cost functions: cancelable and general monotone (both with binary marginal). We show that EFX allocations exist and can be computed for binary cancelable chores, but EFX is incompatible with PO. For general binary marginal functions, we propose an algorithm that computes (partial) envy-free (EF) allocations with at most $n-1$ unallocated items.