Opinion Evolution in Social Networks: Connecting Mean Field Games to Generative Adversarial Nets

Belief and opinion evolution in social networks (SNs) can aid in understanding how people influence others’ decisions through social relationships. As a large number of users are involved in SNs, the complexity of traditional optimization techniques is high as they deal with the interactions between users separately. Moreover, the state variable (opinion) is high-dimensional because a person usually has opinions about many different social issues. Incorporating classical opinion dynamics, we formulate the opinion evolution in SNs as a high-dimensional stochastic mean field game (MFG). Numerical methods for high-dimensional MFGs are practically non-existent because of the need for grid-based spatial discretization. Thus, we propose a machine-learning method to tractably solve high-dimensional stochastic MFGs. With this approach, solving MFGs can be regarded as a special case of training a generative adversarial network. In the simulation, we analyze the effect of random social issues and stubbornness on the opinion evolution. Moreover, with the Social Evolution data set, we show that the proposed algorithm can efficiently predict the diffusion of opinions in SNs.