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Forward-Forward Mean Field Games in Mathematical Modeling with Application to Opinion Formation and Voting Models

Author

Listed:
  • Adriano Festa

    (Politecnico di Torino)

  • Simone Göttlich

    (University of Mannheim)

  • Michele Ricciardi

    (Università Luiss Guido Carli)

Abstract

While the general theory for the terminal-initial value problem in mean-field games is widely used in many models of applied mathematics, the modeling potential of the corresponding forward-forward version is still under-considered. In this work, we discuss some features of the problem in a quite general setting and explain how it may be appropriate to model a system of players that have a complete knowledge of the past states of the system and are adapting to new information without any knowledge about the future. Then we show how forward-forward mean field games can be effectively used in mathematical models for opinion formation and other social phenomena.

Suggested Citation

  • Adriano Festa & Simone Göttlich & Michele Ricciardi, 2025. "Forward-Forward Mean Field Games in Mathematical Modeling with Application to Opinion Formation and Voting Models," Dynamic Games and Applications, Springer, vol. 15(2), pages 664-692, May.
    • Handle: RePEc:spr:dyngam:v:15:y:2025:i:2:d:10.1007_s13235-024-00578-3
    DOI: 10.1007/s13235-024-00578-3
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    References listed on IDEAS

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    1. Jan Lorenz, 2007. "Continuous Opinion Dynamics Under Bounded Confidence: A Survey," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 18(12), pages 1819-1838.
    2. Katarzyna Sznajd-Weron & Józef Sznajd, 2000. "Opinion Evolution In Closed Community," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 11(06), pages 1157-1165.
    3. Hughes, R.L., 2000. "The flow of large crowds of pedestrians," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 53(4), pages 367-370.
    4. Archishman Chakraborty & Parikshit Ghosh & Jaideep Roy, 2020. "Expert-Captured Democracies," American Economic Review, American Economic Association, vol. 110(6), pages 1713-1751, June.
    5. Diogo Gomes & João Saúde, 2014. "Mean Field Games Models—A Brief Survey," Dynamic Games and Applications, Springer, vol. 4(2), pages 110-154, June.
    6. Guillaume Deffuant & Frederic Amblard & Gérard Weisbuch, 2002. "How Can Extremism Prevail? a Study Based on the Relative Agreement Interaction Model," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(4), pages 1-1.
    7. Sznajd-Weron, Katarzyna & Sznajd, Józef, 2005. "Who is left, who is right?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 351(2), pages 593-604.
    8. McKelvey, Richard D., 1976. "Intransitivities in multidimensional voting models and some implications for agenda control," Journal of Economic Theory, Elsevier, vol. 12(3), pages 472-482, June.
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