Contagion in an interacting economy

TL;DR

This paper extends a credit risk model to more general sparse graphs, demonstrating its exact solvability in large networks and connecting it with message-passing methods, with validation through simulations.

Contribution

It generalizes the credit risk model to include heterogeneous agents and degree distributions, providing an exact solution framework for large sparse networks.

Findings

Model is exactly solvable as N approaches infinity.

Message-passing approach accurately describes the model.

Simulation results match theoretical predictions for power-law degree distributions.

Abstract

We investigate the credit risk model defined in Hatchett & K\"{u}hn 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 $N\rightarrow \infty$ 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.