Abstract
We consider a model of influence over a network with finite-horizon opinion dynamics. The network consists of agents that update their opinions via a trust structure as in the DeGroot dynamics. The model considers two potential external influencers that have fixed and opposite opinions. They aim to maximally impact the aggregate state of opinions at the end of the finite horizon by targeting with precision one agent in one specific time period. In the case of only one influencer, we characterize optimal targets on the basis of two features: shift and amplification. Also, conditions are provided under which a specific target is optimal: the maximum-amplification target. In the case of two influencers, we focus on the existence and characterization of pure strategy equilibria in the corresponding two-person strategic zero-sum game. Roughly speaking, if the initial opinions are not too much in favour of either influencer, the influencers’ equilibrium behaviour is also driven by the amplification of targets.
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Notes
Throughout this paper, we adopt the convention that \(W^0=I\), where I denotes the \(n \times n\) identity matrix.
We denote the \(j^{\text {th}}\) unit vector of length n by \(\textbf{e}_j\), where \(\textbf{e}^k_j=1\) if \(k=j\) and \(\textbf{e}^k_j=0\) if \(k \ne j\).
We denote the all-ones vector of length n by \(\textbf{e}\).
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de Vos, W., Borm, P. & Hamers, H. Influencing Opinion Networks: Optimization and Games. Dyn Games Appl (2023). https://doi.org/10.1007/s13235-023-00543-6
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DOI: https://doi.org/10.1007/s13235-023-00543-6