Optimal Efficiency-Envy Trade-Off via Optimal Transport

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Steven Yin, Christian Kroer


We consider the problem of allocating a distribution of items to $n$ recipients where each recipient has to be allocated a fixed, pre-specified fraction of all items, while ensuring that each recipient does not experience too much envy. We show that this problem can be formulated as a variant of the semi-discrete optimal transport (OT) problem, whose solution structure in this case has a concise representation and a simple geometric interpretation. Unlike existing literature that treats envy-freeness as a hard constraint, our formulation allows us to \emph{optimally} trade off efficiency and envy continuously. Additionally, we study the statistical properties of the space of our OT based allocation policies by showing a polynomial bound on the number of samples needed to approximate the optimal solution from samples. Our approach is suitable for large-scale fair allocation problems such as the blood donation matching problem, and we show numerically that it performs well on a prior realistic data simulator.