Who Pays, Who Benefits? Producer-Insurer Games in Life-Saving Medicines

Pharmaceutical markets for life-saving therapies combine monopoly power with insurance coverage. We build a tractable sequential game in which a patent-holder chooses the drug price, a profit-maximising insurer sets its premium, and a population of heterogeneous agents decide whether to insure and, conditional on diagnosis, whether to purchase treatment. Two sufficient statistics - subjective illness probability and reservation price - capture heterogeneity and nest risk-aversion and liquidity-constraint motives within a unified framework. We prove existence of subgame-perfect Nash equilibria and show that entry of an insurer strictly raises producer profits but may raise or lower both drug prices and treatment uptake, depending on the joint distribution of the population statistics. Numerical experiments calibrated to flexible parametric families illustrate non-monotone comparative statics and quantify conditions under which insurance reduces access. Our results provide benchmarks for evaluating price negotiations, price caps, and subsidy schemes in high-cost drug markets.