Shared parking is an important measure to solve the parking difficulty problem. This paper constructs a three-party evolutionary game model involving the shared parking platform, travelers, and parking space owners. By studying the strategy choices and stability of equilibrium points of the participating subjects, it aims to analyze the influencing factors and mechanisms of the choice behavior of each subject. Through simulation with MATLAB software, the results show that: subsidies from the shared parking platform, travelers using shared parking spaces, and owners renting out private parking spaces are the optimal evolutionary strategies for the system. The platform’s subsidy intensity is positively correlated with the willingness of travelers and parking space owners to participate in shared parking; it is appropriate to control the subsidy ratio for travelers around 0.2 and for parking space owners around 0.6. The time cost of shared parking and rental prices are negatively correlated with the willingness of travelers to use shared parking. The potential loss after renting out parking spaces is negatively correlated with the willingness of parking space owners to rent out their spaces, and it is advisable to control the potential loss after renting out parking spaces for owners around 7. The distribution of benefits is positively correlated with the willingness of parking space owners to rent out their spaces. Additionally, the platform is most sensitive to perceived value, followed by parking space owners, and finally travelers. The sensitivity of perceived benefits for the shared parking platform should be controlled around 0.6, and the sensitivity of perceived losses should be controlled around 2.25. This study provides a theoretical basis and guidance for the formulation of shared parking policies, which helps to solve the problem of parking difficulty.