Best-of-Both-Worlds Fairness of the Envy-Cycle-Elimination Algorithm
Jugal Garg, Eklavya Sharma
TL;DR
For two agents, it is shown that a randomized variant of ECE can compute an ex-post EFX and ex-ante envy-free allocation in near-linear time, but for three agents, it is shown that several natural randomization methods for ECE fail to achieve ex-ante proportionality.
Abstract
We consider the problem of fairly dividing indivisible goods among agents with additive valuations. It is known that an Epistemic EFX and $2/3$-MMS allocation can be obtained using the Envy-Cycle-Elimination (ECE) algorithm. In this work, we explore whether this algorithm can be randomized to also ensure ex-ante proportionality. For two agents, we show that a randomized variant of ECE can compute an ex-post EFX and ex-ante envy-free allocation in near-linear time. However, for three agents, we show that several natural randomization methods for ECE fail to achieve ex-ante proportionality.