Estimating risk propagation between interacting firms on inter-firm complex network.

We derive a stochastic function of risk propagation empirically from comprehensive data of chain-reaction bankruptcy events in Japan from 2006 to 2015 over 5,000 pairs of firms. The probability is formulated by firm interaction between the pair of firms; it is proportional to the product of α-th power of the size of the first bankrupt firm and β-th power of that of the chain-reaction bankrupt firm. We confirm that α is positive and β is negative throughout the observing period, meaning that the probability of cascading failure is higher between a larger first bankrupt firm and smaller trading firm. We additionally introduce a numerical model simulating the whole ecosystem of firms and show that the interaction kernel is a key factor to express complexities of spreading bankruptcy risks on real ecosystems.