Consensus on \(p\)-belief communication (Q2761893)

The authors of this interesting paper consider a model containing the following elements: \(N\) is a set of finitely many players and \(i\) denote one player. A state place is a finitely non-empty set, whose members are called states. An event is a subset of the state-space. If \(\Omega \) is a state-space then \(2^{\Omega }\) is the field of all subsets of it. An event \(F\) is said to occur in a state \(\omega \), if \(\omega\in F\). The communication process in the \(p\)-belief system is presented which reaches consensus among many players. They communicate the events that they believe with a probability greater than their own posteriors. It is shown that in the long run each sequence of revised posteriors converges to limiting values and that any two limiting values must be same. The main theorem is that in the \(p\)-belief communication consensus on the limiting values of the posteriors of an event \(X\) can be guaranteed, if the protocol contains no cycle.