The development of fishery carbon sink trading is an important starting point to help China achieve its carbon dioxide emission reduction targets and an inherent requirement for sustainable economic development. However, China’s fishery carbon sink trading market is not yet mature, and the influences of multiple factors have blunted stakeholders’ enthusiasm for market participation. Therefore, it is important to determine the influencing mechanisms of stakeholders’ participation in the fishery carbon sink trading market. In this context, to clarify the factors that affect the enthusiasm of participants, this study establishes a tripartite evolutionary game model of fishery carbon sink trading stakeholders based on the prospect theory. The dynamic evolution trends of the game subjects’ strategies are studied, and the effects of unit fishery carbon sink price, government subsidy ratio, psychological effects of the game subjects, and other factors are discussed. With the development of the fishery carbon sink trading market, the development stages can be divided into initial, medium, and mature stages, and the game players choose different strategies at different stages. Different factors affect the choices of the three parties. When psychological factors involve uncertain gains and losses, they are also important in influencing decision-makers’ decisions.