Game theory has been extensively studied in recent years for its potential benefits on solving interactions between autonomous vehicles in platoon control. In this paper, we propose two behavioral decision-making approach based on non-cooperative game theory with both the complete information and incomplete information for cooperative vehicle platoon systems. The non-cooperative game payoff function takes the platooning performances of economy, comfort, safety, and further achieving self-driving functions into consideration. For the driving situations with incomplete information, a belief pool is constructed to represent the action probability for different behavioral types of vehicles, which will be updated by combining the driving intention identification with a Bayesian probability formula. With this, the stable strategies can be obtained for the two potentially conflicting parties, ensuring that neither of them has a motivation to change their driving behavior. Finally, the simulation results demonstrate that with the proposed behavioral decision-making approaches with complete information, the cooperative platoon performance can be markedly improved; with incomplete information, the platoon can determine the behavioral types of conflicting vehicles and complete collaborative decision-making approaches for solving not only the simple road-rights conflicting problems, but also for the extended vehicle platoon driving scenarios in a more complex transportation system.