Service competition in two-tier healthcare markets with heterogeneous patients balking

Recently, public and private providers within two-tier healthcare markets have engaged in a fierce competition for patients, which is significantly influenced by patients' multifaceted sensitivities to delays and payments, particularly when patients' potential balking is considered. However, existing literature studying the two-tier healthcare market often presupposes patients as homogeneous or one-dimensionally heterogeneous, and neglects their balking behavior. In stark contrast, this paper delves into the combined effects of patients’ delay- and payment-sensitive heterogeneities, alongside their joining or balking decisions, on the service competition dynamics within the two-tier healthcare market. Leveraging a game-theoretic framework, we initially derive subgame equilibria, both inclusive and exclusive of patient balking, uncovering that patient balking can lead to a subgame perfect Nash equilibrium in the presence of two-dimensional patient heterogeneity. Intriguingly, our findings further suggest that the non-profit public provider may, counterintuitively, curtail its service capacity despite budgetary adequacy, contradicting the conventional assumption that such providers would fully allocate funds towards patient care. Ultimately, from a patient welfare standpoint, we find heightened payment heterogeneity discrimination proves detrimental to patients, whereas increased differentiation in delay heterogeneity benefits them. This revelation underscores a pressing social issue inherent in the two-tier healthcare market model: It has the potential to exacerbate healthcare disparities rooted in economic inequalities within the population.