Vehicle-to-vehicle communication enables autonomous platoons to boost traffic efficiency and safety, while ensuring string stability with a constant spacing policy. However, communication-based controllers are susceptible to a range of cyber-attacks. In this paper, we propose a distributed attack mitigation defense framework with a dual-mode control system reconfiguration scheme to prevent a compromised platoon member from causing collisions via message falsification attacks. In particular, we model it as a switched system consisting of a communication-based cooperative controller and a sensor-based local controller and derive conditions to achieve global uniform exponential stability (GUES) as well as string stability in the sense of platoon operation. The switching decision comes from game-theoretic analysis of the attacker and the defender's interactions. In this framework, the attacker acts as a leader that chooses whether to engage in malicious activities and the defender decides which control system to deploy with the help of an anomaly detector. Imperfect detection reports associate the game with imperfect information. A dedicated state constraint further enhances safety against bounded but aggressive message modifications in which a bounded solution may still violate practical constraint e.g. vehicles nearly crashing. Our formulation uniquely combines switched systems with security games to strategically improve the safety of such autonomous vehicle systems.