We study temporal fair division, whereby a set of agents are allocated a (possibly different) set of goods on each day for a period of days. We study this setting, as well as a number of its special cases formed by the restrictions to two agents, same goods on each day, identical preferences, or combinations thereof, and chart out the landscape of achieving two types of fairness guarantees simultaneously: fairness on each day (per day) and fairness over time (up to each day, or the weaker version, overall). In the most general setting, we prove that there always exists an allocation that is stochastically-dominant envy-free up to one good (SD-EF1) per day and proportional up to one good (PROP1) overall, and when all the agents have identical preferences, we show that SD-EF1 per day and SD-EF1 overall can be guaranteed. For the case of two agents, we prove that SD-EF1 per day and EF1 up to each day can be guaranteed using an envy balancing technique. We provide counterexamples for other combinations that establish our results as among the best guarantees possible, but also leaving open some tantalizing questions.

翻译：我们研究时序公平分配问题，其中一组智能体在连续多日内每日被分配一组（可能不同的）物品。我们研究此设定及其若干特殊情形（包括限制为两个智能体、每日物品相同、偏好相同或其组合），并系统探索同时实现两类公平性保证的可能性：每日公平性（每日层面）与跨时公平性（截至每日或更弱的整体层面）。在最一般设定中，我们证明始终存在满足每日随机占优无嫉妒至一物品（SD-EF1）且整体比例性至一物品（PROP1）的分配方案；当所有智能体具有相同偏好时，我们证明可同时保证每日SD-EF1与整体SD-EF1。针对双智能体情形，我们通过嫉妒平衡技术证明可保证每日SD-EF1与截至每日的EF1。我们为其他组合提供了反例，这些反例既表明我们的结果属于可能实现的最佳保证范畴，也留下若干有待探索的开放问题。