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A Mathematical Framework for Dynamical Social Interactions with Dissimulation

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Abstract

Modeling social interactions is a challenging task that requires flexible frameworks. For instance, dissimulation and externalities are relevant features influencing such systems—elements that are often neglected in popular models. This paper is devoted to investigating general mathematical frameworks for understanding social situations where agents dissimulate and may be sensitive to exogenous objective information. Our model comprises a population where the participants can be honest, persuasive, or conforming. Firstly, we consider a non-cooperative setting, where we establish existence, uniqueness and some properties of the Nash equilibria of the game. Secondly, we analyze a cooperative setting, identifying optimal strategies within the Pareto front. In both cases, we develop numerical algorithms allowing us to computationally assess the behavior of our models under various settings.

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Data Availability

All datasets generated in this study can be recovered from information available within the article.

Notes

  1. More precisely, the quotation we refer to is:

    “The checkerboard model in its present form is more of a basic conceptual framework than a model of any given social situation. It has potentiality for further elaboration to fit particular situations. As it now stands, it can be used as a visual representation of the social interaction process, relating attitudes, social interaction and social structure. It should be particularly useful in introductory courses, not only illustrating the relationship among these concepts, but also in discussing the function of models. A model is not necessarily used to predict behavior in a situation. Model building is useful in clarifying the definition of concepts and the relationship among them. Left in verbal form, concepts can be elusive in meaning, whereas computerization require precision in definition of terms. Models can be used to gain insight into basic principles of behavior rather than in finding precise predictions of results for a given social situation, and it is this function which the checkerboard model in its present form provides (...). The checkerboard model provides students of social structure with a possible explanation of its dynamics.”

  2. According to Western metaphysical tradition, “Veritas est adaequatio rei et intellectus”, see St. Thomas Aquinas’ De Veritate, Q.1, A.1-4.

  3. E.g., when a vaccine for a given disease is proven effective, can we observe an anti-vaccine consensus?

  4. This asymmetric interval for the parameters \(\delta _i\) results from our particular parameterization of the model.

  5. For the definition of \(P_{{\mathcal {A}}_i},\) see Remark 1.

  6. https://www.politicalcompass.org/uselection2020.

  7. His actual words were (see Pareto 1896, page 18): “Nous étudierons spécialement l’équilibre économique. Un système économique sera dit en équilibre si le changement d’une des conditions de ce système entraîne d’autres changements qui produiraient une action exactement opposée.”

  8. For the definition of \(P_{{\mathcal {A}}_i},\) see Remark 1.

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Acknowledgements

YS, MOS and YT were financed in part by Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - Brasil (CAPES) - Finance code 001. MOS was also partially financed by CNPq (Grant # 310293/2018-9) and by FAPERJ (Grant # E-26/210.440/2019).

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Authors and Affiliations

  1. Escola de Matemática Aplicada, Fundação Getulio Vargas, Rio de Janeiro, RJ, 22250-900, Brasil

    Yuri F. Saporito

  2. Instituto de Matemática e Estatística, Universidade Federal Fluminense, Niterói, RJ, 24210-200, Brasil

    M. O. Souza & Y. Thamsten

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  1. Yuri F. Saporito
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  2. M. O. Souza
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Correspondence to M. O. Souza.

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Saporito, Y.F., Souza, M.O. & Thamsten, Y. A Mathematical Framework for Dynamical Social Interactions with Dissimulation. J Nonlinear Sci 33, 18 (2023). https://doi.org/10.1007/s00332-022-09867-w

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