Abstract
Artificial intelligence (AI) simulations offer structured, repeatable models for project management, enhancing strategic decision-making under constraints. This study introduces a simulation framework combining AI-driven decision vectors, gamification mechanics, and emergent behaviour models to analyse project execution. The framework employs recursive stack-based dynamics and integrates Agile and Waterfall methodologies to evaluate constraints, risks, governance, and strategic progression. Decision states are modelled as vectors progressing through state-space trajectories, influenced by turn-based decisions. Using Monte Carlo simulation and eigenvalue decomposition, the study demonstrates AI’s decision-learning curves, mirroring human project managers. Initially, AI struggles with complexity but improves through iterative pattern optimisation. Structured AI learning models project trajectories using recursive Fibonacci spirals, enabling predictable execution within emergent, constraint-based environments. Late-game decisions align with dominant eigenvectors, offering scalable methodologies for risk forecasting, strategic alignment, and project optimisation. Eigenvalue decomposition uncovers hidden relationships between decision vectors, revealing emergent learning structures in project execution.