We study a new but simple model for online fair division in which indivisible items arrive one-by-one and agents have monotone utilities over bundles of the items. We consider axiomatic properties of mechanisms for this model such as strategy-proofness, envy-freeness, and Pareto efficiency. We prove a number of impossibility results that justify why we consider relaxations of the properties, as well as why we consider restricted preference domains on which good axiomatic properties can be achieved. We propose two mechanisms that have good axiomatic fairness properties on restricted but common preference domains.

中文翻译：

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单调和在线展会部门

我们研究了一种新的但简单的在线公平划分模型，其中不可分割的物品一个一个地到达，代理对物品的捆绑具有单调效用。我们考虑该模型机制的公理属性，例如策略证明性、免嫉妒性和帕累托效率。我们证明了许多不可能的结果，这些结果证明了为什么我们考虑性质的松弛，以及为什么我们考虑可以实现良好公理性质的受限偏好域。我们提出了两种机制，它们在受限但共同的偏好域上具有良好的公理公平性。