Abstract
Trust is a collective, self-fulfilling phenomenon that suggests analogies with phase transitions. We introduce a stylized model for the build-up and collapse of trust in networks, which generically displays a first order transition. The basic assumption of our model is that whereas trustworthiness begets trustworthiness, panic also begets panic, in the sense that a small decrease in trustworthiness may be amplified and ultimately lead to a sudden and catastrophic drop of collective trust. We show, using both numerical simulations and mean-field analytic arguments, that there are extended regions of the parameter space where two equilibrium states coexist: a well-connected network where global confidence is high, and a poorly connected network where global confidence is low. In these coexistence regions, spontaneous jumps from the well-connected state to the poorly connected state can occur, corresponding to a sudden collapse of trust that is not caused by any major external catastrophe. In large systems, spontaneous crises are replaced by history dependence: whether the system is found in one state or in the other essentially depends on initial conditions. Finally, we document a new phase, in which agents are well connected yet distrustful.
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da Gama Batista, J., Bouchaud, JP. & Challet, D. Sudden trust collapse in networked societies. Eur. Phys. J. B 88, 55 (2015). https://doi.org/10.1140/epjb/e2015-50645-1
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DOI: https://doi.org/10.1140/epjb/e2015-50645-1