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Threshold model with anticonformity under random sequential updating

Author

Listed:
  • Bartłomiej Nowak

    (Wroclaw University of Science and Technology)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

  • Katarzyna Sznajd-Weron

    (Wroclaw University of Science and Technology)

Abstract

We study an asymmetric version of the threshold model of binary decision making with anticonformity under asynchronous update mode that mimics continuous time. We analyze this model on a complete graph using three different approaches: the mean-field approximation, Monte Carlo simulation, and the Markov chain approach. The latter approach yields analytical results for arbitrarily small systems, in contrast to the mean-field approach, which is strictly correct only for an infinite system. We show that for sufficiently large systems, all three approaches produce the same results, as expected. We consider two cases: (1) homogeneous, in which all agents have the same tolerance threshold, and (2) heterogeneous, in which thresholds are given by a beta distribution parameterized by two positive shape parameters α and β. The heterogeneous case can be treated as a generalized model that reduces to a homogeneous model in special cases. We show that particularly interesting behaviors, including social hysteresis and critical mass reported in innovation diffusion, arise only for values of α and β that yield the shape of the distribution observed in reality.

Suggested Citation

  • Bartłomiej Nowak & Michel Grabisch & Katarzyna Sznajd-Weron, 2022. "Threshold model with anticonformity under random sequential updating," PSE-Ecole d'économie de Paris (Postprint) halshs-03688785, HAL.
  • Handle: RePEc:hal:pseptp:halshs-03688785
    DOI: 10.1103/PhysRevE.105.054314
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-03688785
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    Cited by:

    1. Lee, Kyu-Min & Lee, Sungmin & Min, Byungjoon & Goh, K.-I., 2023. "Threshold cascade dynamics on signed random networks," Chaos, Solitons & Fractals, Elsevier, vol. 168(C).

    More about this item

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

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