Belief and Opinion Evolution in Social Networks: A High-Dimensional Mean Field Game Approach

Hao Gao, Alex Lin, Reginald A. Banez, Wuchen Li, Zhu Han, Stanley Osher, H. Vincent Poor

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations


Belief and opinion evolution in social networks (SNs) can aid in understanding how people influence others' decisions through social relationships as well as provide a solid foundation for many valuable social applications. As large numbers 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. To overcome those challenges, 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 based method, where we use an alternating population and agent control neural network (APAC-net), to tractably solve high-dimensional stochastic MFGs. Through APAC-net, solving MFGs can be regarded as a special case of training a generative adversarial network (GAN). To the best of our knowledge, the APAC-Net is the first model that can solve high-dimensional stochastic MFGs. The simulation results affirm the efficiency of the APAC-net.

Original languageEnglish (US)
Title of host publicationICC 2021 - IEEE International Conference on Communications, Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
ISBN (Electronic)9781728171227
StatePublished - Jun 2021
Externally publishedYes
Event2021 IEEE International Conference on Communications, ICC 2021 - Virtual, Online, Canada
Duration: Jun 14 2021Jun 23 2021

Publication series

NameIEEE International Conference on Communications
ISSN (Print)1550-3607


Conference2021 IEEE International Conference on Communications, ICC 2021
CityVirtual, Online

All Science Journal Classification (ASJC) codes

  • Computer Networks and Communications
  • Electrical and Electronic Engineering


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