Distribution of Chores with Information Asymmetry
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Fair distribution of indivisible tasks with non-positive valuations (aka chores) has given rise to a large body of work in recent years. A popular approximate fairness notion is envy-freeness up to one item (EF1), which requires that any pairwise envy can be eliminated by the removal of a single item. While an EF1 and Pareto optimal (PO) allocation of goods always exists and can be computed via several well-known algorithms, even the existence of such solutions for chores remains open, to date. We take an epistemic approach utilizing information asymmetry by introducing dubious chores – items that inflict no cost on receiving agents, but are perceived costly by others. On a technical level, dubious chores provide a more fine-grained approximation of envy-freeness – compared to relaxations such as EF1 – which enables progress towards addressing open problems on the existence and computation of EF1 and PO. In particular, we show that finding allocations with optimal number of dubious chores is computationally hard even for highly restricted classes of valuations. Nonetheless, we prove the existence of envy-free and 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. Our experimental analysis demonstrate that baseline algorithms only require a relatively small number of dubious chores to achieve envy-freeness in practice.
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