Competition between a public and a data-rich private firm: An application to digital health

Digital entrants in health care and health insurance often compete against public or mission-oriented organizations rather than only against private rivals. We develop a Hotelling model of mixed competition in which a private data-rich firm chooses the scope of consumer-data collection and then uses the acquired information to personalize offers. The rival supplies a standard service and is either a welfare-maximizing public firm or a profit-maximizing private firm. We characterize equilibrium data collection, prices, consumer surplus, profits, and social welfare. The private digital firm chooses a wider data-harvesting range when its rival is private than when its rival is public, because a public rival uses welfare-oriented pricing to discipline the induced market allocation rather than to maximize its own profit. The welfare ranking is non-monotonic in the value created by personalization. When the benefit from personalization is either small or large, competition against a public rival yields higher welfare; when the benefit is intermediate, competition against a private rival can dominate because it induces a broader rollout of personalized service. These results highlight that the welfare effects of digital entry depend jointly on data-driven personalization and the ownership objective of incumbent health-sector organizations.