The increasing and exorbitant health care prices in the United States combined with a trend of market concentration has resulted in more than 25 million people being without basic health insurance per year. Increasing mortality rates, decreasing quality of life, preventable hospitalizations, and emergency department overcrowding are some of the consequences of the health care access crisis. This work introduces a bilevel Nash-in-Nash approach to model health care market interactions among insurers, hospitals, and patients. We model eight different scenarios to account for horizontal hospital mergers, insurance network expansions, and SARS-CoV-2 effects over a set of market metrics, such as insurance premiums and quality of care. We use the proposed approach to analyze Hillsborough County in Florida, considering a demand of 1.2 million customers, 14 hospitals, 4 health insurers, and 15 diagnosis-related groups. The results show that the quality of care does not increase with hospital mergers and that improving hospital competition can reduce the current insurance premiums by up to 13.7%. We also found that increasing the number of providers per insurance network reduces the premiums in concentrated hospital markets by up to 35%. Further analyses revealed that the changes in demand due to the SARS-CoV-2 pandemic should reduce insurance premiums (between 25% and 31%) and increase hospital reimbursement rates.