Yankee Swap: A Fast and Simple Fair Allocation Mechanism for Matroid Rank Valuations

We study fair allocation of indivisible goods when agent valuations are matroid rank functions (MRFs). Our main contribution is a simple algorithm based on the colloquial Yankee Swap procedure that computes provably fair and efficient Lorenz dominating allocations. While there exist polynomial time algorithms to compute fair and efficient allocations for MRF valuations, we improve on them in two ways: (a) Our approach is easy to understand and does not use complex matroid optimization algorithms as subroutines. (b) Our approach is scalable; it is provably faster than all known algorithms to compute Lorenz dominating allocations. These two properties are key to the adoption of algorithms in any real fair allocation setting; our contribution brings us one step closer to this goal.