Decision Theory and AI Collusion: How Decision Rules Shape Agentic Collusion

LLM pricing agents can reach above-competitive prices without communicating, but the role of decision-theoretic reasoning remains unclear. We test whether prompting evidential (EDT) or causal (CDT) decision theory, both paired with the premise that rivals are copies of the same model, changes coordination relative to the LLMCartel baseline, with two or three sellers over 10 rounds and four seeds. With three sellers, EDT yields the highest mean profit gain and the widest variation across seeds, and is the only arm with a run near the joint optimum. With two sellers, the control drifts above Nash on its own, and EDT either coordinates from the first rounds or ends at or below Nash. Once collusion forms, removing one agent's EDT paragraph rarely breaks it, while a best-response bot breaks it only after two to four rounds. Traces show CDT agents falling back on twin reasoning, and EDT coordination persisting only when the symmetric argument survives the first low price. Because EDT and CDT share the same-model premise, the effects cannot be attributed to the evidential rule alone.