International Journal For Multidisciplinary Research

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Mathematical Framework for ABM-MARL Integration in Financial Systems: A Discrete Multi-Agent Population-Strategy Game Approach

Author(s) Mr. Manas Ranjan Panda, Bhakta Vashcal Samal
Country India
Abstract Modern financial markets feature complex interactions between vast populations of rule- based agents and adaptive algorithmic traders, yet existing models treat these layers separately. We introduce a discrete-time population-strategy game unifying Agent-Based Modeling (ABM) and Multi-Agent Reinforcement Learning (MARL). The framework’s core innovations are: (1) an asymmetric bilevel architecture where strategic agents optimize over population distributions while endogenously shaping them; (2) a rigorous treatment of system noise via martingale difference processes with bounded moments; and (3) a verifiable, post-convergence spectral stability certificate (ρ(∇µΦ) < 1).
Under mild conditions, we prove:
• Existence of a Mean-Field Equilibrium
• Almost sure convergence of a two-timescale learning dynamic (policy gradient + population dynamics) to this equilibrium
• An O(N−1/2) finite-population approximation error
Our linearly scalable Population-Strategy Policy Gradient (PSPG) algorithm enables tractable computation. We apply the framework to a synthetic market-making environment. Experiments demonstrate emergent critical thresholds (e.g., an 8.2 bps spread bifurcating stable and fragmented regimes in our calibrated model) and a 23% volatility reduction versus a pure ABM system. This framework bridges ABM’s emergent heterogeneity with MARL’s strategic adaptation, addressing key gaps in mean-field game theory and enabling a path toward real-world deployment with verifiable stability.
Keywords Agent-Based Modeling, Multi-Agent RL, Financial Markets, Mean-Field Games, Regulatory AI, Stochastic Approximation, Artificial Intelligence
Field Computer > Artificial Intelligence / Simulation / Virtual Reality
Published In Volume 7, Issue 5, September-October 2025
Published On 2025-09-25
DOI https://doi.org/10.36948/ijfmr.2025.v07i05.54419
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