  Distributed dynamic gossip is a generalization of the classic telephone
problem in which agents communicate to share secrets, with the additional twist
that also telephone numbers are exchanged to determine who can call whom.
Recent work focused on the success conditions of simple protocols such as
"Learn New Secrets" (LNS) wherein an agent a may only call another agent b if a
does not know b's secret. A protocol execution is successful if all agents get
to know all secrets. On partial networks these protocols sometimes fail because
they ignore information available to the agents that would allow for better
coordination. We study how epistemic protocols for dynamic gossip can be
strengthened, using epistemic logic as a simple protocol language with a new
operator for protocol-dependent knowledge. We provide definitions of different
strengthenings and show that they perform better than LNS, but we also prove
that there is no strengthening of LNS that always terminates successfully.
Together, this gives us a better picture of when and how epistemic coordination
can help in the dynamic gossip problem in particular and distributed systems in
general.
