Stackelberg Equilibria in Monopoly Insurance Markets with Probability Weighting

2026-02-18

AI Summary

This study investigates the Stackelberg equilibrium in a monopolistic insurance market where policyholders exhibit probability weighting behavior and the insurer prices contracts using a distorted premium principle. A sequential game is formulated in which the insurer first sets the premium, and the policyholder subsequently selects a contract; both parties’ risk preferences are characterized by distortion functions. Theoretical analysis reveals that the equilibrium contract features a layered structure: full insurance is provided over loss intervals where the policyholder is more pessimistic than the insurer, and no coverage otherwise. Moreover, all Pareto-efficient contracts without welfare loss can be implemented through this equilibrium. Further results show that the equilibrium premium is determined by the policyholder’s marginal willingness to pay for tail losses, and both insurance coverage and insurer profit increase with the policyholder’s degree of risk aversion.

Technology Category

• Game Theory and Economic Paradigms: Equilibrium
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Sequential Decision Making

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: Attacks and countermeasures in recommendation systems

Abstract

We study Stackelberg Equilibria (Bowley optima) in a monopolistic centralized sequential-move insurance market, with a profit-maximizing insurer who sets premia using a distortion premium principle, and a single policyholder who seeks to minimize a distortion risk measure. We show that equilibria are characterized as follows: In equilibrium, the optimal indemnity function exhibits a layer-type structure, providing full insurance over any loss layer on which the policyholder is more pessimistic than the insurer's pricing functional about tail losses; and no insurance coverage over loss layers on which the policyholder is less pessimistic than the insurer's pricing functional about tail losses. In equilibrium, the optimal pricing distortion function is determined by the policyholder's degree of risk aversion, whereby prices never exceed the policyholder's marginal willingness to insure tail losses. Moreover, we show that both the insurance coverage and the insurer's expected profit increase with the policyholder's degree of risk aversion. Additionally, and echoing recent work in the literature, we show that equilibrium contracts are Pareto efficient, but they do not induce a welfare gain to the policyholder. Conversely, any Pareto-optimal contract that leaves no welfare gain to the policyholder can be obtained as an equilibrium contract. Finally, we consider a few examples of interest that recover some existing results in the literature as special cases of our analysis.

Problem

• Stackelberg Equilibrium
• Monopoly Insurance Market
• Probability Weighting
• Distortion Risk Measure
• Pareto Efficiency

Innovation

• Stackelberg equilibrium
• probability weighting
• distortion risk measure
• layer-type indemnity
• monopoly insurance market