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In this paper we address the consensus problem in the context of networkedagents whose communication graph can be split into a certain number of clustersin such a way that interactions between agents in the same clusters arecooperative, while interactions between agents belonging to different clustersare antagonistic. This problem set-up arises in the context of social networksand opinion dynamics, where reaching consensus means that the opinions of theagents in the same cluster converge to the same decision. The consensus problemis here investigated under the assumption that agents in the same cluster havethe same constant and pre-fixed amount of trust (/distrust) to be distributedamong their cooperators (/adversaries). The proposed solution establishes howmuch agents in the same group must be conservative about their opinions inorder to converge to a common decision.

Consensus for Clusters of Agents with Cooperative and Antagonistic Relationships