We investigate how price ceilings and floors affect outcomes in continuous time, double auction markets with discrete goods and multiple qualities. When price controls
exist, the existence of competitive equilibria (the solution concept of classical market theory) is no longer guaranteed; hence, we investigate the nature of non-price
competition and how markets might evolve in its presence. We develop a quality competition model based on matching theory. Equilibria of the quality competition model
always exist in such price-constrained markets; moreover, they naturally correspond to competitive equilibria when competitive equilibria exist. Additionally, we characterize
the set of equilibria of the quality competition model in the presence of price restrictions. In a series of experiments, we find that market outcomes closely conform to the
predictions of the model. In particular, price controls induce non-price competition between agents both in theory and in the experimental environment; market behaviors
result in allocations close to the predictions of the model.