Information Costs and Adverse Selection in Insurance Markets: An Information-Theoretic Model of Risk Classification

This paper develops an information-theoretic model of adverse selection in insurance markets in which insurers use observable risk indices to classify applicants, but must also bear the cost of acquiring and using that information. Following Spence, an index is understood here as an observable characteristic that is correlated with an applicant’s underlying risk type but is not readily manipulated by the applicant. To analyze this problem, the interaction between an insurer and a consumer is modeled as a sequential Bayesian game in which the insurer updates its beliefs about the applicant's risk type after observing an index. The paper links premium determination to the informational content of the index by using mutual information to measure the reduction in uncertainty about the consumer’s risk profile and by incorporating the cost of that information directly into the premium. Within this framework, conditions are derived for a perfect Bayesian equilibrium in which applicants with a favorable index choose to apply for coverage, while applicants with an unfavorable index are discouraged from doing so. Because the index is informative but imperfect, the resulting allocation generally takes the form of a pooling equilibrium rather than full separation. Numerical examples illustrate how the cost of information affects premiums, insurer payoffs, and consumer participation decisions. The paper contributes to the literature on insurance under asymmetric information by showing how information-theoretic tools can be used to model risk classification more explicitly and to clarify the role of information costs in premium setting under adverse selection.