The second simulation builds upon the initial Mean Field Game (MFG) framework by introducing key enhancements to improve the realism, granularity, and interpretive power of the model. It transitions from solving partial differential equations to an agent-based structure, where each investor—retail or institutional—maintains a personalized belief, uncertainty estimate, and dynamically evolving level of overconfidence. This new framework introduces Extended Kalman Filtering (EKF) to model nonlinear signal observations, particularly for retail agents, who receive distorted or sentiment-driven signals. Agents update their beliefs using the appropriate filter and adjust trading behavior accordingly, with trading aggressiveness scaled by their confidence k_{i,t}. These changes allow the model to account for informational asymmetries, diverse learning rates, and sentiment cascades that emerge from herding behavior. The market price is then determined endogenously by aggregating demand across all agents, incorporating behavioral feedback into price evolution. This approach enables simulations of more complex market regimes—bullish, bearish, steady, and volatile—using a stochastic drift model for fundamentals, providing richer insights into how overconfidence interacts with uncertainty and trend direction.

Compared to the first simulation, these enhancements are critical for capturing empirical features of real-world markets. The agent-based formulation introduces heterogeneity in both belief formation and trading strategy, allowing for endogenous clustering of behavior, the emergence of fat-tailed price distributions, and temporally correlated volatility—features commonly observed in financial markets but absent in the earlier PDE-based model. By including confidence bands derived from Kalman posterior variances, the model also visualizes belief uncertainty and how it evolves under different information environments. Most notably, the steady market scenario demonstrates that mispricing can worsen over time purely due to informational ambiguity, rather than volatility or trend—a key insight that highlights the destabilizing role of uncertainty itself. From here, future work will focus on expanding the model’s empirical relevance. This includes calibrating the simulation to real financial data, particularly in the context of speculative bubbles and crash dynamics; testing regime-switching behavior using historical examples such as the 2008 financial crisis or 2020 pandemic onset; and comparing model-generated uncertainty with recent market responses to geopolitical developments like tariff policies. By grounding the model in observable market behavior, it will be possible to assess the predictive validity of overconfidence dynamics and evaluate policy implications for financial stability.