Pareto and Bowley Reinsurance Games in Peer-to-Peer Insurance

2026-02-15

AI Summary

This study addresses the design of reinsurance contracts in peer-to-peer (P2P) insurance, aiming to align the strategic interactions between plan managers and reinsurers to optimize risk sharing and overall welfare. By formulating a game-theoretic model that incorporates a risk-sharing pool and a reinsurer, the authors propose two contract types: a Pareto-optimal cooperative contract grounded in coalition stability, and a Stackelberg-type Bowley contract satisfying pointwise individual rationality constraints, both admitting closed-form solutions. Theoretical analysis reveals that the Bowley contract is never Pareto optimal and consistently yields lower aggregate welfare. Numerical experiments further demonstrate that introducing reinsurance within the Pareto framework significantly enhances welfare, whereas a single premium rate mechanism disproportionately disadvantages high-risk members.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Social and technical mechanisms of refusal for web technologies and applications
• Security and Privacy: Large-scale security measurements

Abstract

We propose a peer-to-peer (P2P) insurance scheme comprising a risk-sharing pool and a reinsurer. A plan manager determines how risks are allocated among members and ceded to the reinsurer, while the reinsurer sets the reinsurance loading. Our work focuses on the strategic interaction between the plan manager and the reinsurer, and this focus leads to two game-theoretic contract designs: a Pareto design and a Bowley design, for which we derive closed-form optimal contracts. In the Pareto design, cooperation between the reinsurer and the plan manager leads to multiple Pareto-optimal contracts, which are further refined by introducing the notion of coalitional stability. In contrast, the Bowley design yields a unique optimal contract through a leader-follower framework, and we provide a rigorous verification of the individual rationality constraints via pointwise comparisons of payoff vectors. Comparing the two designs, we prove that the Bowley-optimal contract is never Pareto optimal and typically yields lower total welfare. In our numerical examples, the presence of reinsurance improves welfare, especially with Pareto designs and a less risk-averse reinsurer. We further analyze the impact of the single-loading restriction, which disproportionately favors members with riskier losses.

Problem

• peer-to-peer insurance
• reinsurance
• strategic interaction
• contract design
• risk allocation

Innovation

• Pareto optimality
• Bowley solution
• peer-to-peer insurance
• reinsurance game
• coalitional stability