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This paper deals with a consensus problem for directed two-layered networks in which dynamics of agents are driven by topologies on both cooperative and competitive graphs. A distributed algorithm for exchanging information between agents in the networks is introduced, where the communication noises are taken into account. A sufficient condition for the proposed algorithm to achieve the socalled ε-averaging consensus, i.e., system state gets arbitrarily close to the average value of agents’ states with desired high probability, is shown. A rigorous stopping rule for the algorithm is also derived. It is shown that all the agents’ states converge to the average value of the initial states when the modeling parameters are chosen appropriately.

Probabilistic Consensus over Directed Two-layered Networks with Communication Noise