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We study cascades on a two-layer multiplex network, with asymmetric feedbackthat depends on the coupling strength between the layers. Based on ananalytical branching process approximation, we calculate the systemic riskmeasured by the final fraction of failed nodes on a reference layer. Theresults are compared with the case of a single layer network that is anaggregated representation of the two layers. We find that systemic risk in thetwo-layer network is smaller than in the aggregated one only if the couplingstrength between the two layers is small. Above a critical coupling strength,systemic risk is increased because of the mutual amplification of cascades inthe two layers. We even observe sharp phase transitions in the cascade sizethat are less pronounced on the aggregated layer. Our insights can be appliedto a scenario where firms decide whether they want to split their business intoa less risky core business and a more risky subsidiary business. In most cases,this may lead to a drastic increase of systemic risk, which is underestimatedin an aggregated approach.

Systemic risk in multiplex networks with asymmetric coupling and threshold feedback