Implementability in Insurance Markets with Adverse Selection

2026-09-25

AI Summary

This study addresses the challenge of incentive-compatible design for premium contract menus in insurance markets with adverse selection by investigating the implementability of retention functions under hidden information. Employing mechanism design theory, it proposes a cyclic monotonicity criterion over general type spaces and establishes it as a necessary and sufficient condition for implementability. Furthermore, a sufficient condition based on submodularity over compact intervals is derived to characterize optimal premium structures. The work achieves a simplified characterization of standard insurance contract classes and validates the proposed approach through numerical examples, thereby providing a rigorous theoretical foundation for mechanism design in insurance markets.

Abstract

We consider an insurance market with hidden information, where the agent's type is private information and is drawn from an arbitrary type space. We discuss the notion of implementability of the collection of retention functions. Namely, how to select premium schedules so that the resulting menu of contracts is incentive compatible, or truthtelling. Specifically, for general type spaces, implementability is equivalent to cyclical monotonicity of the collection of retention functions. For compact interval type spaces, we show that submodularity is a sufficient condition for implementability, under suitable type ordering assumptions. Moreover, for any implementable collection of retention functions, we characterize the corresponding premium schedule. Finally, we apply our results to several standard classes of insurance contracts, for which the general implementability conditions admit simpler characterizations, and we provide several numerical illustrations.

Problem

• Insurance Markets
• Adverse Selection
• Implementability
• Incentive Compatibility
• Hidden Information

Innovation

• adverse selection
• implementability
• cyclical monotonicity
• submodularity
• incentive compatibility