Consensus for Clusters of Agents with Cooperative and Antagonistic Relationships

TL;DR

This paper investigates how networked agents with mixed cooperative and antagonistic relationships can reach consensus within clusters, considering fixed trust levels and the influence of social network structures.

Contribution

It introduces a novel framework for analyzing consensus in clustered networks with both cooperative and antagonistic interactions, accounting for fixed trust/distrust levels.

Findings

Consensus can be achieved within clusters under specified trust conditions

The model quantifies the level of conservativeness needed for convergence

Insights applicable to social networks and opinion dynamics

Abstract

In this paper we address the consensus problem in the context of networked agents whose communication graph can be split into a certain number of clusters in such a way that interactions between agents in the same clusters are cooperative, while interactions between agents belonging to different clusters are antagonistic. This problem set-up arises in the context of social networks and opinion dynamics, where reaching consensus means that the opinions of the agents in the same cluster converge to the same decision. The consensus problem is here investigated under the assumption that agents in the same cluster have the same constant and pre-fixed amount of trust (/distrust) to be distributed among their cooperators (/adversaries). The proposed solution establishes how much agents in the same group must be conservative about their opinions in order to converge to a common decision.