In Multi-Agent Reinforcement Learning (MARL), multiple agents interact with a common environment and with each other, for solving a shared problem in sequential decision-making. Algorithms for MARL have a wealth of application in popular domains including gaming, robotics, and finance. In this work, we study a family of distributed nonlinear stochastic approximation schemes useful in MARL and derive a novel law of iterated logarithm. In particular, our result describes the convergence rate on al…