Multi-Agent Reinforcement Learning Game Model for Market Economic Equilibrium Regulation

Market equilibrium regulation constitutes a dynamic decision-making problem on complex networks, where strategic firms, consumers, platforms, and regulators interact under uncertain demand, delayed price information, and networked spillovers. Although existing multi-agent reinforcement learning (MARL) methods succeed at decentralized adaptation, they typically maximize private rewards without encoding an explicit equilibrium residual or a rigorous link to market clearing. We introduce an Equilibrium-Residual Mirror Multi-Agent Reinforcement Learning (ERM-MARL) framework for regulating market equilibria. The framework formulates a regulated Markov potential game: agents learn pricing, production, and risk-control policies while a dual regulation layer penalizes violations of market clearing, price volatility, and network risk. An equilibrium-residual shaping mechanism aligns each agent’s policy gradient with a global regulation potential. The analysis establishes existence of equilibrium, uniqueness under strong monotonicity, bounded dual stability, and almost-sure convergence of the stochastic mirror actor–critic recursion. Simulation experiments on networked markets demonstrate faster equilibrium-residual decay, higher welfare, lower price volatility, and greater robustness compared with representative MARL and game-learning baselines.