Abstract
We consider the models of average-oriented opinion dynamics. An opinion about an event is distributed among the agents of a social network. There are an optimization problem and two game-theoretical models when players as centers of influence aim to make the opinions of the agents closer to the target ones in a finite time horizon minimizing their costs. The optimization problem and the games of competition for the agents’ opinion are linear-quadratic and solved using the Euler-equation approach. The optimal strategies for optimization problem and the Nash equilibria in the open-loop strategies for the games are found. Numerical simulations demonstrate theoretical results.
Highlights
The new informational aspects of our life allow us to imagine and realize the mechanisms of influences on society’s members and their opinions on some political and other social events
We propose several models with one or two players who compete for the opinion of society members based on DeGroot’s model of information diffusion [1], in which the opinion dynamic is described as a dynamic process where agents or society members can influence each other’s opinions with a given intensity rate at any discrete time
We introduce the models of opinion dynamics when agents, being the members of the network, form their opinions by the influence of the average opinion of the society
Summary
The new informational aspects of our life allow us to imagine and realize the mechanisms of influences on society’s members and their opinions on some political and other social events. We introduce the models of opinion dynamics when agents, being the members of the network, form their opinions by the influence of the average opinion of the society. We consider an optimization problem with one player (a unique center of influence) minimizing costs that depend on the level of influence In this case, there are only two agents in the network, one of them is directly influenced by the player and the other one is influenced by the player via the opinion of the first agent. In all models presented in the paper, the state of the system considered in discrete time is defined by a profile of the opinions of the social network members.
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