Detecting Collusion with Pairwise Net Influence: A Baseline Comparison in Toy Multi-Agent Games

Detecting which AI agents are secretly coordinating is a safety problem for multi-agent systems. Bonjour et al. (2022) proposed detecting collusion with mutual information between agents’ actions, including a measure called pairwise net influence, which subtracts the strongest outside influence on each agent. I implemented this measure for the fully observable simultaneous case and tested whether it identifies the colluding pair better than plain correlation (Cramér’s V), a baseline the paper does not include. I simulated four-agent Rock-Paper-Scissors with one hand-crafted colluding pair whose strength is set by a parameter p. My setup differs from the paper in several ways: four players instead of three, a different collusion rule, no poker or learned agents, and ranking pairs by the smaller of the two directional scores instead of applying a detection threshold. I tested four scenarios (no decoy, hub decoy, chain decoy, separate decoy pair) with 200 trials per setting and 95% Wilson confidence intervals. Both methods ranked the planted pair first almost every time once collusion was strong enough (for example p ≥ 0.6 against a separate decoy of strength 0.5, with 500 rounds), and both performed poorly when collusion was weak. Across 7,200 trials the two methods chose different pairs in only 49 (0.7%), mostly in the hub and chain scenarios, where both were wrong in 34 of the 40 disagreements. I found no evidence that net influence outperforms plain correlation in this simple setting.