This paper presents a strategy that controls the formation of vehicle platoons while driving and maintains the target formation. Before reaching destinations, platoons can be affected by unpredictable factors such as an error in wireless communication, malfunctioning sensors, and weather conditions. These factors can lead to the transformation of platoon formations, with their shapes being randomly determined. Therefore, this paper focuses on returning to the target formation from the randomly determined changes while minimizing the loss of energy savings. To account for this randomness, the model treats unpredictable factors as variables that can affect formation, leading to the development of two mathematical models. Both models have a common purpose of minimizing the loss of energy savings, but one model consists of a platoon directed by the leading vehicle to minimize the loss of energy savings for all vehicles in the platoon, while the other model consists of a platoon in which each agent minimizes its own loss of energy savings. Furthermore, safety for vehicle platoons should be considered when platooning. To consider this, penalties related to velocity that determine the gap between adjacent vehicles are added to the developed model. To identify the most appropriate method for real-world application, simulations are conducted using an algorithm suitable for a stochastic dynamic game, based on the developed mathematical models.