The Coordination Complexity Index: A Parameter-Free Checkpoint Diagnostic for Silent Coordination Failure in Cooperative Multi-Agent Reinforcement Learning

Cooperative multiagent reinforcement learning (MARL) can fail silently while standard reward and loss curves remain inconclusive. This study introduces the Coordination Complexity Index (CCI), a checkpoint statistic with no learned parameters that summarizes dispersion among per-agent greedy Q-values. A frozen checkpoint cannot by itself establish a temporal failure; it can reveal Q-value patterns that motivate further inspection. On Level-Based Foraging (LBF), rules calibrated on the VDN/QMIX/QTRAN triad assign operational high-occupancy, dual-occupancy, and near-zero-dispersion labels, respectively. These labels are not independent proof of stagnation, oscillation, or behavioral roles. The pooled collapsed cohort differs from the non-collapsed LBF cohort by more than four orders of magnitude at the cohort geometric mean, while QMIX attains higher return with lower coordination variance than VDN. Held-out QPLEX falsifies the proposed class-complete-IGM prediction: return is zero, yet C does not approach the collapse cut-off. At 10% of the canonical LBF budget, a retrospective C¯ < 10−3 rule flags all retained QTRAN seeds without flagging retained QMIX seeds; on RWARE it produces at least one environment-induced false positive. CCI is therefore a candidate domain-specific checkpoint screen, not a universal early-stop rule or a coordination-quality score. With the cut-off frozen before evaluation, 5/5 additional QTRAN training seeds remain below it at the retained 10%-budget checkpoint and 5/5 remain below it near 10M steps; this is a positive-class repeatability check, not independent calibration or a new specificity control.

@article{Pothisakha2026,
  title     = {The Coordination Complexity Index: A Parameter-Free Checkpoint Diagnostic for Silent Coordination Failure in Cooperative Multi-Agent Reinforcement Learning},
  journal   = {International Journal of Advanced Computer Science and Applications},
  volume    = {17},
  number    = {9},
  year      = {2026},
  publisher = {The Science and Information Organization},
  author    = {Chatchitsanu Pothisakha and Pudsadee Boonrawd and Siranee Nuchitprasitchai},
  doi       = {10.14569/IJACSA.2026.0170998},
  url       = {https://doi.org/10.14569/IJACSA.2026.0170998}
}