Incentive Pareto Efficiency in Monopoly Insurance Markets with Adverse Selection

Paper: arXiv 2602.09967

Authors: Maria Andraos, Mario Ghossoub

Abstract

We study a monopolistic insurance market with hidden information, where the agent’s type $θ$ 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 $θ$ correspond to more risk-averse types who face stochastically larger losses; whereas (ii) the second assumes that larger values of $θ$ 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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 1.5/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: The paper presents a rigorous theoretical framework establishing the equivalence between incentive Pareto efficiency and social welfare maximization under adverse selection and continuum type spaces. It lacks empirical validation or backtesting as it is purely microeconomic contract theory, but it excels in mathematical rigor and formal completeness.

Research Flowchart

  flowchart TD
    A["Research Goal: Characterize Incentive Pareto Efficient Menus in Monopoly Insurance"] --> B["Inputs: Continuum of types θ, general concave utility / Yaari Dual Utility"]
    B --> C["Methodology: Maximize Social Welfare subject to IC and IR constraints"]
    C --> D["Analysis: Study Type Orderings\n(1: High θ = High Risk & High Risk Aversion\n2: High θ = High Risk & Low Risk Aversion)"]
    D --> E["Key Finding 1: Incentive Efficiency ≡ Social Welfare Maximization for general utilities"]
    D --> F["Key Finding 2 (Yaari Utility): Higher types get higher coverage/premia, Efficiency at Top, Zero Surplus at Bottom"]

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8. Separation Theorem Based on the Quasirelative Interior and Application to Duality Theory (2005)

0 of 84 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.