Contagion in an interacting economy
We investigate the credit risk model defined in Hatchett and Kühn (2006 J. Phys. A: Math. Gen. 39 2231) 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 → ∞ limit and demonstrate that the exact solution is described by the message-passing approach outlined in Karrer and Newman (2010 Phys. Rev. E 82 016101), generalized to include heterogeneous agents and couplings. We provide comparisons with simulations of graph ensembles with power-law degree distributions.