We consider the networked multi-agent reinforcement learning (MARL) problem in a fully decentralized setting, where agents learn to coordinate to achieve joint success. This problem is widely encountered in many areas including traffic control, distributed control, and smart grids. We assume each agent is located at a node of a communication network and can exchange information only with its neighbors. Using softmax temporal consistency, we derive a primal-dual decentralized optimization method and obtain a principled and data-efficient iterative algorithm named {\em value propagation}. We prove a non-asymptotic convergence rate of $\mathcal{O}(1/T)$ with nonlinear function approximation. To the best of our knowledge, it is the first MARL algorithm with a convergence guarantee in the control, off-policy, non-linear function approximation, fully decentralized setting.