Competition and Quality in Regulated Markets: a Differential-Game Approach

We investigate the effect of competition on quality in regulated markets (e.g., health care, higher education, public utilities) taking a differential game approach, in which quality is a stock variable. Using a Hotelling framework, we derive the open-loop solution (providers commit to an optimal investment plan at the initial period) and the feedback closed-loop solution (providers move investments in response to the dynamics of the states). 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: in fact, quality drops to the minimum level in steady state, implying that quality competition is effectively eliminated. In this case, static models tend to exaggerate the positive effect of competition on quality. Our results can explain the mixed empirical evidence on competition and quality for regulated markets.