We study best-of-both-worlds guarantees for the fair division of indivisible items among agents with subadditive valuations. Our main result establishes the existence of a random allocation that is simultaneously ex-ante $\frac{1}{2}$-envy-free, ex-post $\frac{1}{2}$-EFX and ex-post EF1, for every instance with subadditive valuations. We achieve this result by a novel polynomial-time algorithm that randomizes the well-established envy cycles procedure in a way that provides ex-ante fairness. Notably, this is the first best-of-both-worlds fairness guarantee for subadditive valuations, even when considering only EF1 without EFX.

翻译：我们研究在次可加估值下，将不可分割物品公平分配给代理人的双世界最优保证。我们的主要结果证明了对于任意次可加估值实例，存在一种随机分配，同时满足事前$\frac{1}{2}$-无嫉妒、事后$\frac{1}{2}$-EFX和事后EF1。我们通过一种新颖的多项式时间算法实现了这一结果，该算法对成熟的嫉妒循环过程进行随机化，从而提供事前公平性。值得注意的是，这是次可加估值下首个双世界最优公平性保证，即便仅考虑不含EFX的EF1情形也是如此。