We have not found a simple intuitive explanation for this non- existence; but the following observations, prompted by Frank Hahn's note (1974), may be suggestive. The information that is revealed by an individual's choice of an insurance contract depends on all the other insurance policies offered; there is thus a fundamental infor- mational externality that each company, when deciding on which contract it will offer, fails to take into account. Given any set of con- tracts that breaks even, a firm may enter the market using the infor- mational structure implicit in the availability of that set of contracts to make a profit; at the same time it forces the original contracts to make a loss. But as in any Nash equilibrium, the firm fails to take account of the consequences of its actions, and in particular, the fact that when those policies are no longer offered, the informational structure will have changed and it can no longer make a profit.