This paper investigates the problem of age of information (AoI) aware radio resource management for a platooning system. Multiple autonomous platoons exploit the cellular wireless vehicle-to-everything (C-V2X) communication technology to disseminate the cooperative awareness messages (CAMs) to their followers while ensuring timely delivery of safety-critical messages to the Road-Side Unit (RSU). Due to the challenges of dynamic channel conditions, centralized resource management schemes that require global information are inefficient and lead to large signaling overheads. Hence, we exploit a distributed resource allocation framework based on multi-agent reinforcement learning (MARL), where each platoon leader (PL) acts as an agent and interacts with the environment to learn its optimal policy. Existing MARL algorithms consider a holistic reward function for the group's collective success, which often ends up with unsatisfactory results and cannot guarantee an optimal policy for each agent. Consequently, motivated by the existing literature in RL, we propose a novel MARL framework that trains two critics with the following goals: A global critic which estimates the global expected reward and motivates the agents toward a cooperating behavior and an exclusive local critic for each agent that estimates the local individual reward. Furthermore, based on the tasks each agent has to accomplish, the individual reward of each agent is decomposed into multiple sub-reward functions where task-wise value functions are learned separately. Numerical results indicate our proposed algorithm's effectiveness compared with the conventional RL methods applied in this area.