Computing market equilibria is a problem of both theoretical and applied interest. Much research focuses on the static case, but in many markets items arrive sequentially and stochastically. We focus on the case of online Fisher markets: individuals have linear, additive utility and items drawn from a distribution arrive one at a time in an online setting. We define the notion of an equilibrium in such a market and provide a dynamics which converges to these equilibria asymptotically. An important use-case of market equilibria is the problem of fair division. With this in mind, we show that our dynamics can also be used as an online item-allocation rule such that the time-averaged allocations and utilities converge to those of a corresponding static Fisher market. This implies that other good properties of market equilibrium-based fair division such as no envy, Pareto optimality, and the proportional share guarantee are also attained in the online setting. An attractive part of the proposed dynamics is that the market designer does not need to know the underlying distribution from which items are drawn. We show that these convergences happen at a rate of $O(\tfrac{\log t}{t})$ or $O(\tfrac{(\log t)^2}{t})$ in theory and quickly in real datasets.
翻译:电子计算市场平衡是一个理论和适用利益的问题。 大量研究集中在静态案例上, 但在许多市场项目是按顺序和按顺序到达的。 我们关注在线渔业市场的情况: 个人有线性、 添加性效用和从分配中抽取的物品在在线环境中一次到达。 我们定义了这种市场中的平衡概念, 并提供了与这些均衡性相趋合的动态。 市场平衡性的重要使用情况是公平分割的问题。 考虑到这一点, 我们表明我们的动态也可以作为在线项目分配规则使用, 以便时间平均分配和公用事业会与相应的静态渔业市场合并。 这意味着基于市场平衡的公平划分的其他良好特性, 如不嫉妒、 优化性、 比例保障等, 在网上设置中也得到了。 拟议的动态的一个有吸引力的部分是, 市场设计者不需要知道所绘制物品的基本分配情况。 我们显示, 这些趋同在美元(\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\