Intensive video transcoding and data transmission are the most crucial tasks for large-scale Crowd-sourced Livecast Services (CLS). However, there exists no versatile model for joint optimization of computing resources (e.g., CPU) and transmission resources (e.g., bandwidth) in CLS systems, making maintaining the balance between saving resources and improving user viewing experience very challenging. In this paper, we first propose a novel universal model, called Augmented Graph Model (AGM), which converts the above joint optimization into a multi-hop routing problem. This model provides a new perspective for the analysis of resource allocation in CLS, as well as opens new avenues for problem-solving. Further, we design a decentralized Networked Multi-Agent Reinforcement Learning (MARL) approach and propose an actor-critic algorithm, allowing network nodes (agents) to distributively solve the multi-hop routing problem using AGM in a fully cooperative manner. By leveraging the computing resource of massive nodes efficiently, this approach has good scalability and can be employed in large-scale CLS. To the best of our knowledge, this work is the first attempt to apply networked MARL on CLS. Finally, we use the centralized (single-agent) RL algorithm as a benchmark to evaluate the numerical performance of our solution in a large-scale simulation. Additionally, experimental results based on a prototype system show that our solution is superior in saving resources and service performance to two alternative state-of-the-art solutions.