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Limiting behavior of a kindness model

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  • Lanchier, Nicolas
  • Mercer, Max

Abstract

This paper is concerned with a stochastic model for the spread of kindness across a social network. Individuals are located on the vertices of a general finite connected graph, and are characterized by their kindness belief. Each individual, say x, interacts with each of its neighbors, say y, at rate one. The interactions can be kind or unkind, with kind interactions being more likely when the kindness belief of the sender x is high. In addition, kind interactions increase the kindness belief of the recipient y, whereas unkind interactions decrease its kindness belief. The system also depends on two parameters modeling the impact of kind and unkind interactions, respectively. We prove that, when kind interactions have a larger impact than unkind interactions, the system converges to the purely kind configuration with probability tending to one exponentially fast in the large population limit.

Suggested Citation

  • Lanchier, Nicolas & Mercer, Max, 2024. "Limiting behavior of a kindness model," Statistics & Probability Letters, Elsevier, vol. 214(C).
    • Handle: RePEc:eee:stapro:v:214:y:2024:i:c:s0167715224001743
    DOI: 10.1016/j.spl.2024.110205
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    References listed on IDEAS

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    1. Rainer Hegselmann & Ulrich Krause, 2002. "Opinion Dynamics and Bounded Confidence Models, Analysis and Simulation," Journal of Artificial Societies and Social Simulation, Journal of Artificial Societies and Social Simulation, vol. 5(3), pages 1-2.
    2. Guillaume Deffuant & David Neau & Frederic Amblard & Gérard Weisbuch, 2000. "Mixing beliefs among interacting agents," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 3(01n04), pages 87-98.
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