Hierarachical Multiagent Reinforcement Learning for Multi-Group Tax Game

Abstract: Reinforcement learning has increasingly been used to study economic decision-making, such as taxation, public spending, and labour supply. However, most existing RL-based economic models focus on a single government--household group, thereby overlooking the strategic interactions that arise when multiple governments compete while managing their own populations. In practice, many economic systems (e.g., taxation) exhibit a multi-group structure, where each government must optimize its fiscal policy in response not only to household behaviour within its jurisdiction, but also to the policies of other competing governments. To capture this structure, we formulate taxation as a hierarchical multi-group game. Within each group, the interaction between the government and households is modelled as a leader--follower game; across groups, governments are modelled as players in a competitive game. This results in a hybrid hierarchical game that is difficult to solve using standard multi-agent reinforcement learning algorithms. We therefore propose a bi-level training framework built on multi-agent reinforcement learning, together with \textit{ Curriculum Learning} and a \textit{ Closed-Loop Sequential Update} strategy, to stabilize training and promote convergence. We instantiate this framework in a taxation game simulation environment grounded in classical economic models. The environment supports the evaluation of different taxation algorithms and provides multiple economic indicators for assessing policy performance. Experiments show that our approach can learn stable tax policies that benefit all participating groups. Compared with a two-group baseline without the proposed update mechanisms, our method avoids premature game collapse, extends the effective game duration by 60.92\%, produces more sustainable and robust tax policies, and reduces GDP disparities among governments by 44.12\%.