Competitive insurance markets with two unobservables

I study a screening game in a competitive insurance market in which insurance customers differ with respect to both accident probability and degree of risk aversion. It is shown that indifference curves of customers may cross twice; thus the single crossing property does not hold. When differences in risk aversion are sufficiently large, firms cannot use policy deductibles to screen high-risk customers. Types may be pooled in equilibrium or are separated by raising premiums above actuarially fair levels. This leads to excessive entry of firms in equilibrium.