Competitive insurance markets with two unobservables

I study a screening game in a competitive insurance market in which insuran ce 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 i n risk aversion are sufficiently large, firms cannot use policy deductibles to screen high-risk customers. Types may be pooled in equilibrium or are s eparated by raising premiums above actuarially fair levels. This leads to e xcessive entry of firms in equilibrium.