Abstract: This paper introduces a novel framework of dynamic, one-sided incomplete information matching, with strategic interactions, where agents with bounded rationality use case-based decision theory to make predictions about match outcomes. Under a monotonic preference structure, I find that the markets are fairly robust against strategic play. However, in a more relaxed preference environment, the properties of well-studied matching games in static markets, like Deferred Acceptance and Immediate Acceptance, break down. This leads to the result that, under certain conditions, all agents on one side of the market are better off when some agents deviate from their true preference, a product of the new dynamic incentives. Finally, by using a Nadaraya-Watson estimator, I show that the optimal bandwidth varies with the curvature of market outcomes, informing on the predictive ability of the case-based firms, as well as elucidating different market failures.