The French regions have since 1997 for some of them, and since 2002 for the others, to a sponsor of public service for regional travelers, faced with a monopoly of the SNCF. Economic theory and the first assessments show that the monopoly will receive an informational means. One wonders whether the regions are not provided a learning process. To test this hypothesis with a capacity of expertise growing regions, this paper applies to the "TER system" method of surplus accounts and focuses on developments border prices. The detailed examination of the 7 regions, which now have more than ten years experience of agreements with the SNCF, shows that they were able to control the evolution of border prices. But they could not avoid the shock, pre...