Repeatedly Matching Items to Agents Fairly and Efficiently

We consider a novel setting where a set of items are matched to the same set of agents repeatedly over multiple rounds. Each agent gets exactly one item per round, which brings interesting challenges to finding efficient and/or fair repeated matchings. A particular feature of our model is that the value of an agent for an item in some round depends on how often the item has been used by the agent in the past. We present a set of positive and negative results about the efficiency and fairness of repeated matchings.