Minimum coverage regulation in insurance markets

We study the consequences of imposing a minimum coverage in an insurance market where enrollment is mandatory and agents have private information on their true risk type. If the regulation is not too stringent, the equilibrium is separating in which a single insurer monopolizes the high risks while the rest attract the low risks, all at positive profits. Hence individuals, regardless of their type, "subsidize" insurers. If the legislation is sufficiently stringent the equilibrium is pooling, all insurers just break even and low risks subsidize high risks. None of these results require resorting to non-Nash equilibrium notions