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Opinion Dynamics and Stubbornness Via Multi-Population Mean-Field Games

Author

Listed:
  • Dario Bauso

    (University of Sheffield
    Università di Palermo)

  • Raffaele Pesenti

    (Università Ca’ Foscari Venezia)

  • Marco Tolotti

    (Università Ca’ Foscari Venezia)

Abstract

This paper studies opinion dynamics for a set of heterogeneous populations of individuals pursuing two conflicting goals: to seek consensus and to be coherent with their initial opinions. The multi-population game under investigation is characterized by (i) rational agents who behave strategically, (ii) heterogeneous populations, and (iii) opinions evolving in response to local interactions. The main contribution of this paper is to encompass all of these aspects under the unified framework of mean-field game theory. We show that, assuming initial Gaussian density functions and affine control policies, the Fokker–Planck–Kolmogorov equation preserves Gaussianity over time. This fact is then used to explicitly derive expressions for the optimal control strategies when the players are myopic. We then explore consensus formation depending on the stubbornness of the involved populations: We identify conditions that lead to some elementary patterns, such as consensus, polarization, or plurality of opinions. Finally, under the baseline example of the presence of a stubborn population and a most gregarious one, we study the behavior of the model with a finite number of players, describing the dynamics of the average opinion, which is now a stochastic process. We also provide numerical simulations to show how the parameters impact the equilibrium formation.

Suggested Citation

  • Dario Bauso & Raffaele Pesenti & Marco Tolotti, 2016. "Opinion Dynamics and Stubbornness Via Multi-Population Mean-Field Games," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 266-293, July.
    • Handle: RePEc:spr:joptap:v:170:y:2016:i:1:d:10.1007_s10957-016-0874-5
    DOI: 10.1007/s10957-016-0874-5
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    Cited by:

    1. Paolo Dai Pra & Elena Sartori & Marco Tolotti, 2023. "Polarization and Coherence in Mean Field Games Driven by Private and Social Utility," Journal of Optimization Theory and Applications, Springer, vol. 198(1), pages 49-85, July.
    2. Li, Tingyu & Zhu, Hengmin, 2020. "Effect of the media on the opinion dynamics in online social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 551(C).
    3. Paolo Dai Pra & Elena Sartori & Marco Tolotti, 2019. "Climb on the Bandwagon: Consensus and Periodicity in a Lifetime Utility Model with Strategic Interactions," Dynamic Games and Applications, Springer, vol. 9(4), pages 1061-1075, December.

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