Given the growing amount of medical litigation heard by courts, the 2002 Kouchner law in France has created the Office National d'Indemnisation des Accidents Médicaux (ONIAM), whose main aim is to encourage out-of-court settlements when a conflict between a physician and the victim of a medical accident occurs. More than 10 years after the implementation of this law, the statistics analysing its effectiveness are contradictory, which raises the question of the potential negative effects of the ONIAM on the compensation system. In order to address this question, the article analyses the impact of the ONIAM on the nature of settlement negotiations between the physician and the victim. Using a dynamic game within incomplete information, we develop a comparative analysis of two types of compensation systems in case of medical accidents: socialised financing granted by the ONIAM and private financing provided by the physician. We show that the ONIAM could encourage out-of-court settlements provided that the hypothesis of judicial error is relevant. On the contrary, in the case of a low probability of judicial errors, the ONIAM could be effective only for severe medical accidents.