Classic market design theory is rooted in static models where all participants trade simultaneously. In contrast, modern platform-mediated digital markets are fundamentally dynamic, defined by the asynchronous and stochastic arrival of supply and demand. This chapter surveys recent work that brings market design to this dynamic setting. We focus on a methodological framework that transforms complex dynamic problems into tractable static programs by analyzing the long-run stationary distribution of the system. The survey explores how priority rules and information policy can be designed to clear markets and screen agents when monetary transfers are unavailable, and, when they are available, how queues of participants and goods can be managed to balance intertemporal mismatches of demand and supply and to spread competitive pressures across time.
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