Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection

2026-02-10

AI Summary

This study addresses adverse selection in a monopolistic insurance market where the insured’s private type—continuous and unobservable—affects both loss distribution and risk preferences. The paper investigates the design of incentive-compatible contracts that maximize social welfare. It establishes, for the first time, an equivalence between incentive compatibility and social welfare maximization under this setting. Within Yaari’s dual theory of choice under risk, the authors combine mechanism design, variational analysis, and optimal control techniques to derive a semi-explicit solution for the optimal contract menu. The results show that higher types receive greater coverage and pay higher premiums, the lowest type earns no information rent, and the highest type achieves full insurance. The structure of the optimal contracts critically depends on the social welfare weights assigned to different types.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Decision/Utility Theory

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: User privacy protection in personalized systems

Abstract

We study a monopolistic insurance market with hidden information, where the agent's type $\theta$ is private information that is unobservable to the insurer, and it is drawn from a continuum of types. The hidden type affects both the loss distribution and the risk attitude of the agent. Within this framework, we show that a menu of contracts is incentive efficient if and only if it maximizes social welfare, subject to incentive compatibility and individual rationality constraints. This equivalence holds for general concave utility functionals. In the special case of Yaari Dual Utility, we provide a semi-explicit characterization of optimal incentive-efficient menus of contracts. We do this under two different settings: (i) the first assumes that types are ordered in a way such that larger values of $\theta$ correspond to more risk-averse types who face stochastically larger losses; whereas (ii) the second assumes that larger values of $\theta$ correspond to less risk-averse types who face stochastically larger losses. In both settings, the structure of optimal incentive-efficient menus of contracts depends on the level of the social welfare weight. Moreover, at the optimum, higher types receive greater coverage in exchange for higher premia. Additionally, optimal menus leave the lowest type indifferent, with the insurer absorbing all surplus from the lowest type; and they exhibit efficiency at the top, that is, the highest type receives full coverage.

Problem

• Incentive Pareto Efficiency
• Monopoly Insurance Market
• Adverse Selection
• Hidden Information
• Social Welfare

Innovation

• Incentive Pareto Efficiency
• Adverse Selection
• Monopoly Insurance
• Yaari Dual Utility
• Optimal Contract Menu