  Cooperation is often implicitly assumed when learning from other agents.
Cooperation implies that the agent selecting the data, and the agent learning
from the data, have the same goal, that the learner infer the intended
hypothesis. Recent models in human and machine learning have demonstrated the
possibility of cooperation. We seek foundational theoretical results for
cooperative inference by Bayesian agents through sequential data. We develop
novel approaches analyzing consistency, rate of convergence and stability of
Sequential Cooperative Bayesian Inference (SCBI). Our analysis of the
effectiveness, sample efficiency and robustness show that cooperation is not
only possible in specific instances but theoretically well-founded in general.
We discuss implications for human-human and human-machine cooperation.
