Emergent coordination without symmetry breaking in Minority Game via policy-based reinforcement learning

Unlike classical game-theoretic models that rely on deductive reasoning and strategic foresight, the Minority Game (MG) provides an inductive learning framework where agents adapt based solely on past outcomes. This simple yet powerful model has become a canonical setting for exploring decentralized coordination in competitive environments. Recently, reinforcement learning (RL) methods – most notably the value-based Q-learning algorithm – have been introduced into the MG framework to improve learning flexibility and resource efficiency. However, Q-learning relies on forward-looking value estimation and is therefore deductive in nature, which runs counter to the inductive philosophy of the MG. Moreover, such value-based methods often induce symmetry breaking and role polarization. In this work, we revisit the MG using another category of RL: the policy-based approach. Specifically, we employ a modified REINFORCE algorithm that eliminates future reward prediction and maintains stochastic, continuous updates of agent policies. Remarkably, this form of smooth adaptation gives rise to a novel coordination pattern — one that achieves global efficiency and suppressed volatility, yet preserves statistical symmetry. Through macroscopic, microscopic, and network-level analysis, we identify this coordination as one where agents remain individually stochastic, while weak anti-correlated patterns sustain decentralized coherence. These results highlight a qualitatively distinct mode of emergent self-organization: symmetry-preserving, distributed, and enabled by the smooth adaptation of policy-based learning.