When Does Net Influence Catch Colluders? Replication and Stress Tests of an Information-Theoretic Collusion Detector

Bonjour, Aggarwal and Bhargava (UAI 2022) proposed pairwise net influence, a conditional-mutual-information statistic that flags two agents as colluding when each influences the other more than any third agent does. The method is a candidate black-box auditor for multi-agent systems, but no public implementation exists and it has not been stress-tested. We re-implement it from the paper’s equations and reproduce its iterated Rock–Paper–Scissors results: with logs in bits and the previous round’s joint action as the state, our detection accuracy matches the paper’s Table 2 within a few percentage points. We then probe three failure modes in simulation. (1) The fixed threshold α = 0.05 fixes a minimum detectable collusion strength (collusion probability ≈ 0.195, derived analytically); weaker collusion is never flagged, even after 10,000 rounds, while it also produces up to 41% false positives on short logs. A G-test with Bonferroni correction keeps false positives near 5% at every sample size and detects collusion probability 0.1 in 96–97% of runs at 3,000–10,000 rounds. (2) Two agents with no agreement that follow a shared public signal are flagged by both detectors (95–100% at signal-following probability 0.5) unless the signal is included in the conditioning state. (3) A three-agent coalition defeats the net- influence rule (≤ 38.5% detection), because subtracting the strongest other influence cancels coalition members against each other; a dependency graph of significant pairs recovers the coalition in 95.5–100% of runs. All experiments are CPU-only simulations with hand-coded agents; we did not test LLM agents.