On the existence of EFX (and Pareto-optimal) allocations for binary chores

Biaoshuai Tao, Xiaowei Wu, Ziqi Yu, Shengwei Zhou

Abstract: We study the problem of allocating a set 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, EFX and Pareto-optimal (PO) allocations can be computed in polynomial time. We further consider more general cost functions: cancelable, submodular, and general (with binary marginal). For binary cancelable chores, we show that EFX allocations can be computed in polynomial time, but EFX is incompatible with PO. For submodular and general functions (with binary marginals), we propose algorithms for the computation of approximate EFX and envy-free (EF) (partial) allocations with at most n−1<math><mi is="true">n</mi><mo linebreak="goodbreak" linebreakstyle="after" is="true">−</mo><mn is="true">1</mn></math> unallocated items respectively.