Designing a Smart Health Insurance Pricing System: Integrating XGBoost and Repeated Nash Equilibrium in a Sustainable, Data-Driven Framework

Designing fair and sustainable pricing mechanisms for health insurance requires accurate risk assessment and the formulation of incentive-compatible strategies among stakeholders. This study proposes a hybrid framework that integrates machine learning with game theory to determine optimal, risk-based premium rates. Using a comprehensive dataset of insured individuals, the XGBoost algorithm is employed to predict medical claim costs and calculate corresponding premiums. To enhance transparency and explainability, SHAP analysis is conducted across four risk-based groups, revealing key drivers, including healthcare utilization and demographic features. The strategic interactions among the insurer, insured, and employer are modeled as a repeated game. Using the Folk Theorem, the conditions under which long-term cooperation becomes a sustainable Nash equilibrium are explored. The results demonstrate that XGBoost achieves high predictive accuracy (R2 ≈ 0.787) along with strong performance in error measures (RMSE ≈ 1.64 × 107 IRR, MAE ≈ 1.08 × 106 IRR), while SHAP analysis offers interpretable insights into the most influential predictors. Game-theoretic analysis further reveals that under appropriate discount rates, stable cooperation between stakeholders is achievable. These findings support the development of equitable, transparent, and data-driven health insurance systems that effectively align the incentives of all stakeholders.