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.