Nash Peer-to-Peer Insurance Bargaining under Price Fairness and Coalitional Stability

2026-08-10

AI Summary

This study addresses the optimal contract design for risk-averse participants in peer-to-peer (P2P) insurance under constraints of price fairness and coalition stability. Building upon an asymmetric Nash bargaining framework and incorporating the expected value premium principle, the authors develop a computable contract model that satisfies a uniform loading fairness criterion and prevents sub-coalition deviations. Through axiomatic analysis, they demonstrate the superiority of this approach over conventional weighted-sum methods and derive analytical structures for full, partial, and zero reinsurance scenarios. Theoretical results establish the existence and uniqueness of the optimal contract. Numerical experiments reveal that price fairness effectively mitigates disparities in risk allocation, while group welfare exhibits non-monotonic dependence on coalition size, highlighting the critical role of dynamically evolving bargaining power.

Abstract

We study peer-to-peer (P2P) insurance contracting between a risk-averse P2P reinsurer and multiple risk-averse peers in an asymmetric Nash-bargaining framework, where all agents seek to improve expected utility relative to their disagreement points. Consistent with the expected value premium principle, we impose a price-fairness condition requiring each peer's expected contribution to be based on a common loading applied to the peer's expected loss. To justify the bargaining formulation relative to a standard fixed-weight weighted-sum optimization problem, we provide an axiomatic characterization showing that the Nash bargaining solution satisfies properties well suited to voluntary P2P insurance contracting in small pools. We establish the existence and uniqueness of the optimal contract and derive first-order characterizations for the full-, partial-, and zero-reinsurance regimes. To address subgroup formation, we develop computationally tractable sufficient conditions that rule out viable coalitional deviations, both with and without price fairness. Our numerical study investigates the impact of price fairness and pool size on the optimal contract and agents' welfare. Price fairness reduces dispersion in risk allocations and certainty-equivalent loadings among peers. Regarding pool size, welfare need not increase monotonically, highlighting that risk-pool expansion depends not only on diversification but also on the evolution of bargaining power.

Problem

• peer-to-peer insurance
• Nash bargaining
• price fairness
• coalitional stability
• risk allocation

Innovation

• Nash bargaining
• peer-to-peer insurance
• price fairness
• coalitional stability
• asymmetric risk aversion