Eur. Phys. J. B (2015) 88: 55
https://doi.org/10.1140/epjb/e2015-50645-1

Regular Article

Sudden trust collapse in networked societies

¹ Chaire de Finance Quantitative, Laboratoire de Mathématiques Appliquées aux Systèmes, École Centrale Paris, 92290 Châtenay-Malabry, France
² Capital Fund Management, 23 rue de l’Université, 75007 Paris, France
³ Encelade Capital SA, EPFL Innovation Park, Bâtiment C, 1015 Lausanne, Switzerland

^a e-mail: joao.batista@ecp.fr

Received: 22 September 2014
Received in final form: 23 January 2015
Published online: 9 March 2015

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.