We study a model of dynamic combinatorial assignment of indivisible objects without money. We introduce a new solution concept called ``dynamic approximate competitive equilibrium from equal incomes'' (DACEEI), which stipulates that markets must approximately clear in almost all time periods. A naive repeated application of approximate competitive equilibrium from equal incomes (Budish, 2011) does not yield a desirable outcome because the approximation error in market-clearing compounds quickly over time. We therefore develop a new version of the static approximate competitive equilibrium from carefully constructed random budgets which ensures that, in expectation, markets clear exactly. We then use it to design the ``online combinatorial assignment mechanism'' (OCAM) which implements a DACEEI with high probability. The OCAM is (i) group-strategyproof up to one object (ii) envy-free up to one object for almost all agents (iii) approximately market-clearing in almost all periods with high probability when the market is large and arrivals are random. Applications include refugee resettlement, daycare assignment, and airport slot allocation.

翻译：我们研究了无货币环境下不可分割物品的动态组合分配模型。我们提出了一种称为"动态近似平等收入竞争均衡"（DACEEI）的新解概念，该概念要求市场在几乎所有时间段内近似出清。由于市场出清的近似误差会随时间快速累积，对近似平等收入竞争均衡（Budish，2011）进行简单的重复应用并不能产生理想结果。因此，我们基于精心构建的随机预算，开发了一种新型静态近似平等收入竞争均衡，确保市场在期望意义下精确出清。随后，我们利用该均衡设计了"在线组合分配机制"（OCAM），该机制能够以高概率实现DACEEI。OCAM具有以下特性：(i) 对于最多一个物品具有群体策略稳定性；(ii) 对于几乎所有参与者，对于最多一个物品具有无嫉妒性；(iii) 在市场规模较大且到达随机的情况下，几乎所有时间段内以高概率实现近似市场出清。该机制的应用包括难民安置、日托分配和机场时刻分配。