Health and medical data sharing and trading are important issues in the coordinated governance of healthcare services, medical insurance, and pharmaceuticals. To examine sharing incentives and transaction acceptance, this study develops a two-population asymmetric evolutionary game model of data sharing between primary healthcare institutions and Grade A tertiary hospitals, and an evolutionary game model of transactions between healthcare institutions and pharmaceutical companies under predetermined high and low price offers. Equilibrium stability analysis and numerical simulations are conducted. The results show that, when the sharing strategies of the two types of healthcare institutions are complementary, an increase in one group’s sharing proportion raises the other group’s relative payoff from sharing. Additional governance costs reduce the relative payoff from sharing; stable full sharing requires the incremental sharing benefits of both primary healthcare institutions and Grade A tertiary hospitals to exceed their respective additional governance costs. Under the baseline assumption that both price offers entail the same costs, subsidies, and application benefits, the system converges to the “high-price sharing–price acceptance” equilibrium from any interior initial state when the research and development subsidy exceeds its critical value. Stability analysis shows that, with other parameters held constant, an increase in coordination benefits, innovation output premiums, or alternative data acquisition costs lowers this critical value. Accordingly, this paper proposes improving transaction incentives aligned with data application benefits, strengthening data standardization and quality evaluation, and promoting coordinated governance across departments.