Characterizing Agent-Based Model Dynamics via $ε$-Machines and Kolmogorov-Style Complexity

We propose a two-level information-theoretic framework for characterizing the informational organization of Agent-Based Model (ABM) dynamics within the broader paradigm of Complex Adaptive Systems (CAS). At the macro level, a pooled $\epsilon$-machine is reconstructed as a reference model that summarizes the system-wide informational regime. At the micro level, $\epsilon$-machines are reconstructed for each caregiver-elder dyad and variable, and are complemented with algorithm-agnostic Kolmogorov-style measures, including normalized LZ78 complexity and bits per symbol from lossless compression. The resulting feature set $\{h_{\mu}, C_{\mu}, E, \mathrm{LZ78}, \mathrm{bps}\}$ enables distributional analysis, stratified comparisons, and unsupervised clustering across agents and scenarios. This dual-scale design preserves agent heterogeneity while providing an interpretable macro-level baseline, aligning ABM practice with CAS principles of emergence, feedback, and adaptation. A case study on caregiver-elder interactions illustrates the framework's implementation; the results and discussion will be completed following final simulation runs.