Applying Reinforcement Learning (RL) to economic modeling reveals a fundamental tension: standard RL agents do not behave as competitive price-takers. While macroeconomic models typically assume agents take aggregate conditions as given, a naive single-agent RL algorithm learns to internalize its impact on the environment, effectively exerting market power. We illustrate this divergence in a search-and-matching model with concave production, showing that a standard RL agent converges to a monopsonistic allocation rather than the competitive equilibrium. Furthermore, we show that RL's approach to time discounting distorts standard intertemporal economic trade-offs. To resolve these issues, we propose a Calibrated Mean-Field Reinforcement Learning framework that restricts the agent to optimize against an exogenous aggregate state to restore price-taking behavior, and recalibrates the RL reward structure to reflect true economic opportunity costs. By iteratively updating the aggregate state, our algorithm converges to a stationary fixed point that recovers the competitive equilibrium. This approach provides a method for embedding learning algorithms into dynamic general equilibrium models.
This paper presents a residual-constrained topology optimization framework that controls interface transition bandwidth without requiring external density filters. The steady conserved Allen--Cahn (AC) equation is formulated as an equality residual constraint and solved via a mass-weighted Augmented Lagrangian Method (ALM) coupled with the Method of Moving Asymptotes (MMA). A closed-form chemical potential projection eliminates the constant residual mode, ensuring algebraic compatibility with external volume targets. Variational sensitivity analysis reveals a symmetric-plus-rank-one Jacobian that yields matrix-free sensitivities without additional adjoint PDE solves, reducing residual sensitivity overhead to only 0.11% of the state elasticity solve time in 3D. Systematic 2D benchmarks confirm that interface bandwidth is governed intrinsically by reaction--diffusion parameters across mesh refinements. While diffuse interfaces incur a continuous compliance elevation (1.4%--12.3%), a volume-preserving 0/1 post-processing audit across 48 benchmark cases demonstrates that this gap stems primarily from intermediate-density penalization: binarized AC-ALM designs achieve equal or superior stiffness in 45 configurations (averaging 1.2% stiffer than SIMP). Simultaneously, single-node hinges and strut fragmentation are substantially suppressed compared to unregularized baselines. Three-dimensional benchmarks further demonstrate practical spatial viability for complex structures.