General characterization of the action–probability communication gap

Characterize, in general, when and why probability communication yields an advantage over action communication in multi-agent collaboration with partitioned information.

Background

The paper proves a separation between action-only and probability communication in a specific chained-parity model, where probability messages preserve intermediate posterior states while action messages collapse them. The authors explicitly state that the broader conditions governing this gap have not been characterized. Resolving this problem would extend the theoretical results beyond the stylized chained-parity setting and clarify which information structures and decision problems make calibrated probability exchange beneficial.