Equilibrium in a Competitive Insurance Market Under Adverse Selection with Endogenous Information

But when the information structure itself is endogenous - firms and consumers decide what information about insurance purchases to reveal to whom - there always exists a Nash equilibrium. Strategies for firms consist of insurance contracts to offer and information-revelation strategies; for customers - buying as well as information revelation strategies. The equilibrium set of insurance contracts is unique: the low risk individual obtains insurance corresponding to the pooling contract most preferred by him; the high risk individual, that plus (undisclosed) supplemental insurance at his own actuarial odds resulting in his being fully insured. Equilibrium information revelation strategies of firms entail some but not complete information sharing. However, in equilibrium all individuals are induced to tell the truth