Fair Division with Minimal Sharing

A five-minute rump-session talk at the COMSOC Video Seminar. When indivisible goods may be shared, how few goods need to be shared to reach an allocation that is envy-free and fractionally Pareto optimal? Sandomirskiy and Segal-Halevi showed this can be answered efficiently for a fixed number of agents whose valuations are not too similar. I pose an open problem about what happens as the number of agents grows, and preview a hardness result for envy-free, fractionally Pareto-optimal allocations from joint work with Aditi Sethia.