Ramp merging is considered as one of the major causes of traffic congestion and accidents because of its chaotic nature. With the development of connected and automated vehicle (CAV) technology, cooperative ramp merging has become one of the popular solutions to this problem. In a mixed traffic situation, CAVs will not only interact with each other, but also handle complicated situations with human-driven vehicles involved. In this paper, a game theory-based ramp merging strategy has been developed for the optimal merging coordination of CAVs in the mixed traffic, which determines dynamic merging sequence and corresponding longitudinal/lateral control. This strategy improves the safety and efficiency of the merging process by ensuring a safe inter-vehicle distance among the involved vehicles and harmonizing the speed of CAVs in the traffic stream. To verify the proposed strategy, mixed traffic simulations under different penetration rates and different congestion levels have been carried out on an innovative Unity-SUMO integrated platform, which connects a game engine-based driving simulator with a traffic simulator. This platform allows the human driver to participate in the simulation, and also equip CAVs with more realistic sensing systems. In the traffic flow level simulation test, Unity takes over the sensing and control of all CAVs in the simulation, while SUMO handles the behavior of all legacy vehicles. The results show that the average speed of traffic flow can be increased up to 110%, and the fuel consumption can be reduced up to 77%, respectively.