Massachusetts Institute of Technology Cambridge United States
We now define a mathematical framework for networks. Let G V,E be an undirected random network graph drawn from a known distribution pG,1 composed of a finite vertex set V and a link set E V x V modulo S where S i j j i. Each vertex i isin V corresponds to an agent, and each link j i isin E corresponds to a channel by which information flows from agent j to agent i in the network. We denote the neighborhood of I by Ni j vertical line i j isin E.There is a state internal or external W drawn from a distribution pW that the agents may want to estimate, transmit, and act upon. Each agent i also possesses a state and some private observation about W. We denote the state at time t by xit, and we assume that the tuple of initial states xi0 is correlated with W and are drawn randomly from a joint distribution pWX0 . Agent is private informationobservation at time t is denoted by Yit and has a joint distribution pWYit with W. Finally, agent i has some information about agent js state either because it can observe it or agent j transmits it, which we denote by mjit mjixjt.