Blockchain technology promotes the efficiency and transparency of the shipping supply chain, presenting new opportunities and challenges for various maritime stakeholders. To enhance the application of blockchain in the shipping industry, a vertical game model is constructed, involving a port and a shipping company (SP), to analyze the roles of maritime stakeholders and cooperative investment strategies. The study also investigates the impact of time value, investment cost, and blockchain operating cost on price, demand, and profit. Comparative analyses and numerical experiments provide insights into the equilibrium strategy and "free ride" behavior among stakeholders in blockchain adoption. Results indicate: (1) When the time value is higher, investment in blockchain benefits the SP regardless of the blockchain operating cost. The high-efficiency port (HP) should cooperate with the high-time-value SP in blockchain technology investment, while the low-efficiency port (LP) should cooperate with the low-time-value SP. (2) When the blockchain operating cost is lower, the port and the SP are more inclined to cooperate in blockchain technology investment. As the blockchain operating cost increases, the SP becomes proactive in investing to drive blockchain adoption, while the port "free rides". The SP only exhibits a "free ride" motive when the time cost is low. These findings offer valuable insights for maritime stakeholders in making decisions regarding blockchain adoption.