Fairly Allocating Many Goods with Few Queries
This addresses the computational efficiency of fair allocation in resource division, with incremental improvements in query complexity for specific agent and utility settings.
The paper tackles the problem of fairly allocating many indivisible goods with minimal queries, showing that for two agents with arbitrary monotonic utilities, an EF1 allocation can be computed using a logarithmic number of queries, and similar bounds hold for three agents, suggesting practical feasibility for large numbers of goods.
We investigate the query complexity of the fair allocation of indivisible goods. For two agents with arbitrary monotonic utilities, we design an algorithm that computes an allocation satisfying envy-freeness up to one good (EF1), a relaxation of envy-freeness, using a logarithmic number of queries. We show that the logarithmic query complexity bound also holds for three agents with additive utilities, and that a polylogarithmic bound holds for three agents with monotonic utilities. These results suggest that it is possible to fairly allocate goods in practice even when the number of goods is extremely large. By contrast, we prove that computing an allocation satisfying envy-freeness and another of its relaxations, envy-freeness up to any good (EFX), requires a linear number of queries even when there are only two agents with identical additive utilities.