Our research project is structured around three themes. The first concerns the impact of competition on the complementary health insurance market. Our analysis is based on a distinction between the individual and collective markets. The second theme explored herein deals with the adequacy between demand expectations and supply proposals. The third and final section concerns representative case studies of regulatory failure or success, and the effect thereof on market structure. One example is the gradual elimination of designation clauses, which were considered by the Constitutional Council as a brake on competition between insurers and an infringement of contractual freedom as of Juen 13, 2013. This reform constitutes a relevant case study on the consequences and effectiveness of regulation, for example, by analyzing the capture of demand on the collective market.