This study investigates the evolutionary game dynamics among electric vehicle distribution entities in the context of shared charging facilities, addressing the critical issue of inadequate charging resources. To understand the behavior of different stakeholders under government incentive policies, we develop an evolutionary game model involving a government department and two logistics enterprises (A and B). Through stability analysis, we explore equilibrium conditions of evolutionarily stable strategies (ESSs) for the tripartite evolutionary game. To ensure the robustness of our findings, we conduct a MATLAB simulation analysis to validate the analytical results. Our findings highlight that government subsidies, the costs incurred by logistics enterprises to share charging facilities, and the additional distribution income derived from this sharing are critical in determining whether the evolutionary game can achieve a stable equilibrium state. This research enables logistics companies to optimize the use of charging resources, lower operating costs, and enhance delivery efficiency. Additionally, government subsidy policies play a crucial role in encouraging logistics enterprises to engage in charging facility sharing, thereby fostering the sustainable development of the entire logistics industry. Based on these insights, the paper offers practical recommendations to further promote the sharing of charging facilities in electric vehicle distribution.