Shore power represents one of the principal solutions for the green transformation within the port industry. It significantly aids in the reduction in carbon emissions from vessels while they are berthed in port, yet often necessitates an effective promotional strategy to foster its installation and utilization. Stakeholders including port authorities, ship operators, and local governments all play a crucial role in achieving this objective. This paper employs a tripartite evolutionary game model in conjunction with a system dynamics model to investigate the evolutionary responses of stakeholders when policy tools are applied, and consequently, to elucidate the dynamics of strategy effectiveness. In this context, six business scenarios are developed to ascertain the potential impacts of implementing subsidies and carbon taxes. The findings demonstrate that any singular strategy, whether a subsidy or a carbon tax, is inadequate for the successful advancement of shore power; on the contrary, a government-led, integrated, and dynamic reward–punishment strategy aids in stabilizing the inherent fluctuations within this game process. Moreover, the initial willingness of ship operators exerts a considerably greater influence than that of the other two stakeholders.