We investigate the effect of competition on quality in health care markets with regulated prices taking a differential game approach, in which quality is a stock variable. Using a Hotelling framework, we derive the open-loop solution (health care providers set the optimal investment plan at the initial period) and the feedback closed-loop solution (providers move investments in response to the dynamics of the states). Under the closed-loop solution competition is more intense in the sense that providers observe quality in each period and base their investment on this information. If the marginal provision cost is constant, the open-loop and closed-loop solutions coincide, and the results are similar to the ones obtained by static models. If the marginal provision cost is increasing, investment and quality are lower in the closed-loop solution (when competition is more intense). In this case, static models tend to exaggerate the positive effect of competition on quality.