Asymptotic agreement in distributed estimation

Each of several agents updates his estimate of the same random variable whenever he makes a new observation or receives the estimate made by another agent. In turn, each agent transmits his estimate to a randomly chosen subset of the other agents. A subset of agents forms a communicating ring if for every pair m, p of ring members, there is a sequence of ring members m = m₁, m₂,. . . , m₍+₁ = p such that m₈ sends his estimate to m₈+₁ infinitely often. If each ring member knows that he is a ring member, then the estimates of all the ring members asymptotically agree. However, this common limit can depend upon the order in which estimates are transmitted.