Explicit size distributions of failure cascades redefine systemic risk on finite networks

Social contagion induced by uncertain information

Information and individual activities often spread globally through the network of social ties. While social contagion phenomena have been extensively studied within the framework of threshold models, it is common to make an assumption that may be violated in reality: each individual can observe the neighbors' states without error. Here, we analyze the dynamics of global cascades under uncertainty in an otherwise standard threshold model. Each individual uses statistical inference to estimate the probability distribution of the number of active neighbors when deciding whether to be active, which gives a probabilistic threshold rule. Unlike the deterministic threshold model, the spreading process is generally nonmonotonic, as the inferred distribution of neighbors' states may be updated as a new signal arrives. We find that social contagion may occur as a self-fulfilling event in that misperception may trigger a cascade in regions where cascades would never occur under certainty.

Predicting the cascading dynamics in complex networks via the bimodal failure size distribution

Cascading failure as a systematic risk occurs in a wide range of real-world networks. Cascade size distribution is a basic and crucial characteristic of systemic cascade behaviors. Recent research works have revealed that the distribution of cascade sizes is a bimodal form indicating the existence of either very small cascades or large ones. In this paper, we aim to understand the properties and formation characteristics of such bimodal distribution in complex networks and further predict the final cascade size. We first find that the bimodal distribution is ubiquitous under certain conditions in both synthetic and real networks. Moreover, the large cascades distributed in the right peak of bimodal distribution are resulted from either the failure of nodes with high load at the first step of the cascade or multiple rounds of cascades triggered by the initial failure. Accordingly, we propose a hybrid load metric (HLM), which combines the load of the initial broken node and the load of failed nodes triggered by the initial failure, to predict the final size of cascading failures. We validate the effectiveness of HLM by computing the accuracy of identifying the cascades belonging to the right and left peaks of the bimodal distribution. The results show that HLM is a better predictor than commonly used network centrality metrics in both synthetic and real-world networks. Finally, the influence of network structure on the optimal HLM is discussed.

The Downside of Heterogeneity: How Established Relations Counteract Systemic Adaptivity in Tasks Assignments

We study the lock-in effect in a network of task assignments. Agents have a heterogeneous fitness for solving tasks and can redistribute unfinished tasks to other agents. They learn over time to whom to reassign tasks and preferably choose agents with higher fitness. A lock-in occurs if reassignments can no longer adapt. Agents overwhelmed with tasks then fail, leading to failure cascades. We find that the probability for lock-ins and systemic failures increase with the heterogeneity in fitness values. To study this dependence, we use the Shannon entropy of the network of task assignments. A detailed discussion links our findings to the problem of resilience and observations in social systems.

Modeling financial distress propagation on customer-supplier networks

Financial networks have been the object of intense quantitative analysis during the last few decades. Their structure and the dynamical processes on top of them are of utmost importance to understand the emergent collective behavior behind economic and financial crises. In this paper, we propose a stylized model to understand the "domino effect" of distress in client-supplier networks. We provide a theoretical analysis of the model, and we apply it to several synthetic networks and a real customer-supplier network, supplied by one of the largest banks in Europe. Besides, the proposed model allows us to investigate possible scenarios for the functioning of the financial distress propagation and to assess the economic health of the full network. The main novelty of this model is the combination of two stochastic terms: an additive noise, accounting by the capability of trading and paying obligations, and a multiplicative noise representing the variations of the market. Both parameters are crucial to determining the maximum default probability and the diffusion process characteristics.

Efficient message passing for cascade size distributions

How big is the risk that a few initial failures of networked nodes amplify to large cascades that endanger the functioning of the system? Common answers refer to the average final cascade size. Two analytic approaches allow its computation: (a) (heterogeneous) mean field approximation and (b) belief propagation. The former applies to (infinitely) large locally tree-like networks, while the latter is exact on finite trees. Yet, cascade sizes can have broad and multi-modal distributions that are not well represented by their average. Full distribution information is essential to identify likely events and to estimate the tail risk, i.e. the probability of extreme events. We therefore present an efficient message passing algorithm that calculates the cascade size distribution in finite networks. It is exact on finite trees and for a large class of cascade processes. An approximate version applies to any network structure and performs well on locally tree-like networks, as we show with several examples.