Title: Revisiting Higher-Order Gradient Methods for Multi-Agent Reinforcement Learning. Abstract: This paper revisits Higher-Order Gradient (HOG) methods for Multi-Agent Reinforcement Learning (MARL). HOG methods are algorithms in which agents use higher-order gradient information to account for other agents' anticipated learning, and are shown to improve coordination in games with self-interested agents. So far, however, HOG methods are only applied to games with low-dimensional state spaces due to inefficient computation and preservation of higher-order gradient information. In this work, we solve these limitations and propose a HOG framework that can be applied to games with higher-dimensional state spaces. Moreover, we show that current HOG methods, when applied to games with common-interested agents, i.e., team games, can lead to miscoordination between the agents. To solve this, we propose Hierarchical Reasoning (HR) to improve coordination in team games, and we experimentally show that our proposed HR significantly outperforms state-of-the-art methods in standard multi-agent games. With our contributions, we greatly improve the applicability of HOG methods for MARL. For reproducibility, the code used for our work will be shared after the reviewing process.