Non-Stationarity Breaks Permutation Surrogates in Multi-Agent Reinforcement Learning: Diagnosis and Remedies

arXiv:2604.23716v5 Announce Type: replace-cross Abstract: Reporting guidance for information-theoretic measures is rarely tested against ground truth. We test one guardrail in two multi-agent reinforcement learning games, a social dilemma and a coordination race, where directed influence between selected agent pairs is zero by construction, over 100 seeds. Omitting one precondition, exclusion of the non-stationary training transient, gives false-positive rates of 100.00% and 99.95%: agents annealing exploration independently, in runs that never met, are flagged as influencing one another. Excluding the transient reaches 3.05% in the social dilemma but 11.8% in the coordination game, so the non-stationarity must be treated and exclusion is neither the only way nor sufficient. What we recommend instead changes the null model. Series, statistic and estimand are left untouched: permuting the source within blocks of training time reaches 5.25% and 5.50%, the only one of the three at or below the size of the test in both games. The construction is not new, being a restricted permutation local to blocks of training time; the measurement is. A third null control, four learners in the social dilemma, defeats all three, and there conditioning costs three times what ours does, 15.20 points against 4.55. Titrating injected links separates it from conditioning on identical pairs, 82.5% against 58.0%, while the ablated test reports a positive with or without a link, so its apparent sensitivity is uninformative. Five block counts spanning 16 to 256 land in the nominal region. Code and data are released.