Exact Is Easier: Credit Assignment for Cooperative LLM Agents

Credit assignment for a team of LLM agents, what each message was worth, has mostly been treated as prediction: a learned critic, a trajectory-level score, or an agent ablation stands in for the counterfactual that defines credit, which is rarely run. Teams that communicate through a shared context are different: when everything a downstream agent reads is written into the trace, the trace is the state, and that counterfactual can be executed. A credit signal can then be judged as any estimator is: by bias, variance, and agreement with an independent reference. C3, credit assignment by counterfactual continuation, substitutes one message at a decision point and continues the run to the terminal reward, so its credit is unbiased, exact up to Monte Carlo error. Given the sampled alternatives, that error's variance follows a derived law with no term for the number of agents, and the observed noise follows the law on 6 workflows of 2 to 10 decision points. On the 2-agent chain, from 4 continuations, C3 ranks alternatives at 0.69 rank correlation against a 16-continuation reference, near the 0.73 at which 2 such references agree; a critic trained on the same rollouts reaches 0.29. Used as the advantage in training a 2-agent team, C3 beats MAGRPO, the stronger baseline in our comparison, and spends 37% fewer training tokens than MAPPO, since only the messages downstream of a decision point are regenerated. When the trace is the state, credit need not be predicted; it can be exact.