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Bounded confidence dynamics and graph control enforcing consensus

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Document pages: 26 pages

Abstract: A generic feature of bounded confidence type models is the formation ofclusters of agents. We propose and study a variant of bounded confidencedynamics with the goal of inducing unconditional convergence to a consensus.The defining feature of these dynamics, which we name the No one left behinddynamics, is the introduction of a local control on the agents which preservesthe connectivity of the interaction network. We rigorously demonstrate thatthese dynamics result in unconditional convergence to a consensus. Thequalitative nature of our argument prevents us quantifying how fast a consensusemerges, however we present numerical evidence that sharp convergence rateswould be challenging to obtain for such dynamics. Finally, we propose a relaxedversion of the control. The dynamics that result maintain many of thequalitative features of the bounded confidence dynamics yet ultimately stillconverge to a consensus as the control still maintains connectivity of theinteraction network.

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