Sudden Trust Collapse in Networked Societies

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.

The evolving cobweb of relations among partially rational investors

“…Coevolving networks have been recently used in social sciences as a useful tool to model situations in which the a feedback mechanism modifies the structure of the network in dependence of the state of the nodes, see for instance [ 31 , 37 , 38 , 56 – 60 ]. On the ground of our numerical results, and supported by the encouraging matching between the outcome of our model, common sense intuition, and a typical influence network, we envision that the coevolving dynamical networks paradigm, might represent a useful tool to generate more realistic models also in the analysis of financial markets.…”

“…However, in real markets the influence among the agents may be dynamic [ 32 , 33 ] thus determining an adaptive topology whose evolution may be driven, for instance, by the perceived successfulness of the agents, with some central nodes of the network loosing their leadership in favor of other agents that are climbing the market [ 34 – 36 ]. State-dependent probabilistic laws have been used to couple the evolution of the agents’ state with network dynamics in socioeconomic phenomena, such as the diffusion of trust or technological expertise [ 37 , 38 ]. Differently form the existing literature, we model network evolution in financial markets though the dynamical systems paradigm, so as to reproduce the effect of memory in social dynamics [ 39 ].…”