A gossip protocolGossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocolGossip protocol is a telephone call wherein the caller and the callee 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 some 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 already know that all agents are experts, do not make and do not answer calls. We also model that such protocols are common knowledgeCommon knowledge among the agents. We investigate conditions under which such gossip protocolsGossip protocol 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 protocol with missed calls can terminate faster than the same protocol without missed calls. (shrink)

A gossip protocol is a procedure for sharing secrets in a network. The basic action in a gossip protocol is a pairwise message exchange (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. We also (...) investigate gossip protocols that are common knowledge among the agents. Additionally, we model that agents who are super experts do not make and do not answer calls, and that this is common knowledge. 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 commonly known protocol without engaged agents. (shrink)