We interpret solving the multi-vehicle routing problem as a team Markov game with partially observable costs. For a given set of customers to serve, the playing agents (vehicles) have the common goal to determine the team-optimal agent routes with minimal total cost. Each agent thereby observes only its own cost. Our multi-agent reinforcement learning approach, the so-called multi-agent Neural Rewriter, builds on the single-agent Neural Rewriter to solve the problem by iteratively rewriting solutions. Parallel agent action execution and partial observability require new rewriting rules for the game. We propose the introduction of a so-called pool in the system which serves as a collection point for unvisited nodes. It enables agents to act simultaneously and exchange nodes in a conflict-free manner. We realize limited disclosure of agent-specific costs by only sharing them during learning. During inference, each agents acts decentrally, solely based on its own cost.First empirical results on small problem sizes demonstrate that we reach a performance close to the employed OR-Tools benchmark which operates in the perfect cost information setting.