SIAM Journal on Computing, Volume 49, Issue 1, Page 206-243, January 2020.
We initiate the study of the communication complexity of fair division with indivisible goods. We focus on some of the most well studied fairness notions (envy-freeness, proportionality, and approximations thereof) and valuation classes (submodular, subadditive, and unrestricted). We show that for more than two players (and any combination of other parameters), determining whether a fair allocation exists requires exponential communication (in the number of goods). For two players, tractability depends heavily on the specific combination of parameters, and most of the paper is focused on the two-player setting. Taken together, our results completely resolve whether the communication complexity of computing a fair allocation (or determining that none exists) is polynomial or exponential, for every combination of fairness notion, valuation class, and number of players, for both deterministic and randomized protocols.

中文翻译：

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离散公平司的沟通复杂性

SIAM计算杂志，第49卷，第1期，第206-243页，2020年1月。
我们开始研究不可分割商品的公平划分的沟通复杂性。我们关注一些研究最深​​入的公平概念（嫉妒自由，成比例及其近似）和评估类别（次模块化，次加性和非限制性）。我们表明，对于两个以上的参与者（以及其他参数的任意组合），确定是否存在公平分配需要指数沟通（以商品数量计）。对于两个玩家，可处理性在很大程度上取决于参数的特定组合，并且大多数论文都集中在两个玩家的设置上。两者合计，我们的结果完全解决了对于公平概念，评估类别，