Distribution of Chores with Information Asymmetry

Hadi Hosseini, Joshua Kavner, Tomasz Was, Lirong Xia

Abstract: One well-regarded fairness notion in dividing indivisible chores is envy-freeness up to one item (EF1), which requires that pairwise envy can be eliminated by the removal of a single item. While an EF1 and Pareto optimal (PO) allocation of goods can always be found via well-known algorithms, even the existence of such solutions for chores remains open, to date. We take an epistemic approach to identify such allocations utilizing information asymmetry by introducing dubious chores - items that inflict no cost on receiving agents but are perceived to be costly by others. On a technical level, dubious chores provide a more fine-grained approximation of envy-freeness than EF1. We show that finding allocations with minimal number of dubious chores is computationally hard. Nonetheless, we prove the existence of envy-free and fractional PO allocations for n agents with only 2n-2 dubious chores and strengthen it to n-1 dubious chores in four special classes of valuations.