Optimal Coinsurance Strategies in Health Insurance Systems: An Actuarial and Game-Theoretic Analysis

• Published in: International journal of applied and computational mathematics Vol. 11; no. 6; p. 237
• Main Authors: Abgarmi, Mohammadreza Barati, Najafabadi, Amir T. Payandeh, Zokaei, Mohammad
• Format: Journal Article
• Language: English
• Published: New Delhi Springer India 01.12.2025; Springer Nature B.V
• Subjects: Adverse selection; Applications of Mathematics; Coinsurance; Computational Science and Engineering; Costs; Decision making; Equilibrium; Game theory; Health insurance; Health services; Inequality; Insurance; Insurance coverage; Insurance industry; Insurance premiums; Lagrange multiplier; Mathematical and Computational Physics; Mathematical Modeling and Industrial Mathematics; Mathematics; Mathematics and Statistics; Moral hazard; Nuclear Energy; Operations Research/Decision Theory; Optimization; Original Paper; Pharmaceuticals; Preventive medicine; Random variables; Sensitivity analysis; Stakeholders; Theoretical; Utility functions; Iran; Primary 62F15; Coinsurance; Stackelberg game; 91B05; 91G99; Cost sharing; Game theory; 62E15; Health insurance system
• ISSN: 2349-5103; 2199-5796
• DOI: 10.1007/s40819-025-02054-x

This study develops a structured framework for determining optimal coinsurance rates in a multi-stakeholder health insurance system involving the government, social insurers, private insurers, and individuals. Using an actuarial approach within a Stackelberg game-theoretic model, we address a key gap in prior research by jointly optimizing the objectives of all stakeholders rather than focusing on single-agent models. The model shows that without moral hazard and adverse selection, full insurance coverage (i.e., zero out-of-pocket payments) minimizes the mean squared error in premium estimation for private insurers, while complete budget allocation by the government toward healthcare expenses reduces service overutilization. Numerical analyses, based on real-world pharmaceutical cost data, compare coinsurance policies of 0%, 10%, and 20%, revealing that in this case study, lower coinsurance consistently leads to better alignment with optimal insurer strategies. Sensitivity analyses further demonstrate the dominant influence of administrative costs on the optimal loading factor and premium setting.