Mechanisms for Trading Durable Goods

We consider trading indivisible and easily transferable \emph{durable goods}, which are goods that an agent can receive, use, and trade again for a different good. This is often the case with books that can be read and later exchanged for unread ones. Other examples of such easily transferable durable goods include puzzles, video games and baby clothes. We introduce a model for the exchange of easily transferable durable goods. In our model, each agent owns a set of items and demands a different set of items. An agent is interested in receiving as many items as possible from his demand set. We consider mechanisms that exchange items in cycles in which each participating agent receives an item that he demands and gives an item that he owns. We aim to develop mechanisms that have the following properties: they are \emph{efficient}, in the sense that they maximize the total number of items that agents receive from their demand set, they are \emph{strategyproof} (i.e., it is in the agents' best interest to report their preferences truthfully) and they run in \emph{polynomial time}. One challenge in developing mechanisms for our setting is that the supply and demand sets of the agents are updated after a trade cycle is executed. This makes constructing strategyproof mechanisms in our model significantly different from previous works, both technically and conceptually and requires developing new tools and techniques. We prove that simultaneously satisfying all desired properties is impossible and thus focus on studying the tradeoffs between these properties. To this end, we provide both approximation algorithms and impossibility results.