The Folk Theorem establishes that collusion can be sustained in repeated interactions, yet empirical evidence suggests coordination becomes more difficult as market participants increase. This thesis presents the first test of whether Large Language Model (LLM) agents exhibit this pattern. In controlled experiments with 2–5 competing agents, we find LLM coordination erodes predictably with competition. Our results show a 3.7% reduction in equilibrium price for each additional firm (p < 0.001), with prices declining smoothly. This culminates in a 10.6% total price reduction from duopoly to five-agent markets, providing quantitative evidence on algorithmic collusion boundaries in the AI era.
