Steering Opinion through Dynamic Stackelberg Optimization

Abstract: This paper employs the Friedkin-Johnsen (FJ) model to describe the dynamics of opinion evolution within a social network. Under the FJ framework, the society is divided into two subgroups that include stubborn agents and regular agents. The opinions of stubborn agents are not influenced by regular agents, whereas the opinions of regular agents evolve based on the opinions of their neighboring agents. By defining the origin as the desired collective opinion of the society, the objective of the paper is to minimize deviations from this desired opinion. To achieve this, a Stackelberg game is established between the stubborn and regular subgroups, where the opinion adjustments of the stubborn agents and the openness variables of regular agents serve as the decision variables. The proposed solution approach integrates quadratic programming and dynamic programming to optimize these decision variables at each discrete time step using forward and backward propagation.