An Investment Framework for Continuous Time Opinion Dynamics on Networks

The literature on investment strategies for steering opinion dynamics on networks primarily focuses on discrete time models. This work proposes an investment framework for a continuous time model that captures essential factors, such as opinion bias, network effect, and camp investment, by extending Friedkin–Johnsen and Taylor's models. We, hence, devise an optimal investment strategy in the presence of various constraints and present its properties, such as memorylessness. We also show that there is a certain adaptability benefit even in the asymptotic regime. When the network structure and the values of the model parameters are not known, we study the learning aspect in two scenarios: first, when opinions of all the nodes are observable, and second, when opinions of a sample set of nodes are observable. We conclude with a simulation study on representative real-world networks and present insights. When all the nodes' opinions are observable, we show that our learning algorithm deduces the exact optimal strategy in very few intervals. When opinions of a sample set of nodes are observable, our learning algorithm is highly accurate and robust for a large enough sample size.