Contagion in an interacting economy

Abstract

We investigate the credit risk model defined in Hatchett & Kühn under more general assumptions, in particular using a general degree distribution for sparse graphs. Expanding upon earlier results, we show that the model is exactly solvable in the $N\to \infty$ limit and demonstrate that the exact solution is described by the message-passing approach outlined by Karrer and Newman, generalized to include heterogeneous agents and couplings. We provide comparisons with simulations of graph ensembles with power-law degree distributions.

arXiv comment21 pages, 6 figures

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• Uncovering the non-equilibrium stationary properties in sparse Boolean networks
• Overcoming the complexity barrier of the dynamic message-passing method in networks with fat-tailed degree distributions