Connectivity and automation provide the opportunity to enhance safety and mitigate congestion in transportation systems. In fact, these technologies can enhance the efficiency of drivers/vehicles' decision-making by managing and coordinating the interactions among human-driven and connected, automated vehicles. Such management and coordination can lead to developing a collaborative connected, automated driving environment. Game theory, as a methodology to model the outcome of the interactions among multiple players, is a perfect tool to characterize the interaction between these vehicles. One of the most challenging maneuvers to model is drivers/vehicles' tactical decisions at intersections. Focusing on unprotected left turn maneuvers, this study aims at developing a game theory based framework to characterize driver behavior in unprotected left turn maneuvers in a connected, automated driving environment. A two-person non-zero-sum non-cooperative game under complete information is selected to model the underlying decision-making. NGSIM data is used to calibrate the payoff functions based on Maximum Likelihood Estimation. Validation results indicate that this framework can effectively capture vehicle interactions when performing conflicting turning movements while achieving a relatively high accuracy in predicting vehicles' real choice.