We consider optimal intervention in the Elliott-Golub-Jackson network model \cite{jackson14} and we show that it can be transformed into an influence maximization-like form, interpreted as the reverse of a default cascade. Our analysis of the optimal intervention problem extends well-established targeting results to the economic network setting, which requires additional theoretical steps. We prove several results about optimal intervention: it is NP-hard and cannot be approximated to a constant factor in polynomial time. In turn, we show that randomizing failure thresholds leads to a version of the problem which is monotone submodular, for which existing powerful approximations in polynomial time can be applied. In addition to optimal intervention, we also show practical consequences of our analysis to other economic network problems: (1) it is computationally hard to calculate expected values in the economic network, and (2) influence maximization algorithms can enable efficient importance sampling and stress testing of large failure scenarios. We illustrate our results on a network of firms connected through input-output linkages inferred from the World Input Output Database.

翻译：本文考虑Elliott-Golub-Jackson网络模型中的最优干预问题，并证明该问题可转化为类影响力最大化形式，可被解释为违约级联的逆向过程。通过对最优干预问题的分析，我们将成熟的定位研究结论拓展至经济网络场景，这需要额外的理论推导步骤。我们证明了关于最优干预的若干结论：该问题属于NP难问题，且无法在多项式时间内实现常数因子近似逼近。进一步研究表明，随机化失效阈值可使问题转化为单调子模形式，从而可应用多项式时间内具有强大逼近性能的现有算法。除最优干预外，本文还展示了分析结果对其它经济网络问题的实际应用价值：(1)经济网络中期望值的计算存在计算困难性；(2)影响力最大化算法可实现对大规模失败场景的高效重要性抽样与压力测试。我们通过基于世界投入产出数据库推断的投入产出关联企业网络对结论进行了实证验证。