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The threshold model with anticonformity under random sequential updating
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The threshold model with anticonformity under random sequential updating

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Abstract

We study an asymmetric version of the threshold model with anticonformity under asynchronous update mode that mimics continuous time. We study this model on a complete graph using three different approaches: 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 the thresholds are given by a beta distribution parametrized by two positive shape parameters alpha and béta. 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, arise only for values of alpha and béta that yield the shape of the distribution observed in real social systems

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  • Bartlomiej Nowak & Michel Grabisch & Katarzyna Sznajd-Weron, 2022. "The threshold model with anticonformity under random sequential updating," Documents de travail du Centre d'Economie de la Sorbonne 22004, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    • Handle: RePEc:mse:cesdoc:22004
    DOI: 10.1103/PhysRevE.105.054314
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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

    Keywords

    opinion dynamics; threshold model; anticonformity; mean-field approximation; Markov chain;
    All these keywords.

    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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