Everyone Knows that Everyone Knows: Gossip Protocols for Super Experts
  A gossip protocol is a procedure for sharing secrets in a network. The basic
action in a gossip protocol is a telephone call wherein the calling agents
exchange all the secrets they know. An agent who knows all secrets is an
expert. The usual termination condition is that all agents are experts.
  Instead, we explore protocols wherein the termination condition is that all
agents know that all agents are experts. We call such agents super experts.
Additionally, we model that agents who are super experts do not make and do not
answer calls. Such agents are called engaged agents. We also model that such
gossip protocols are common knowledge among the agents. We investigate
conditions under which protocols terminate, both in the synchronous case, where
there is a global clock, and in the asynchronous case, where there is not. We
show that a commonly known protocol with engaged agents may terminate faster
than the same protocol without engaged agents.
