Beating the Logarithmic Barrier for the Subadditive Maximin Share Problem

We study the problem of fair allocation of indivisible goods for subadditive agents. While constant-MMS bounds have been given for additive and fractionally subadditive agents, the best existential bound for the case of subadditive agents is 1/O(log n log log n). In this work, we improve this bound to a 1/O((log log n)2)-MMS guarantee. To this end, we introduce new matching techniques and rounding methods for subadditive valuations that we believe are of independent interest and will find their applications in future work.