How Shapley Value and Its Generalizations Can Help in the Analysis of Complex Engineering Systems and What Next

For a complex engineering system – such as a city’s street network – it is important to predict how its functionality is decreased when some of these components break down, and, if repairs are needed and repairs budget is limited, which subset of the set of components should be repaired first to maximize the resulting functionality. For systems with a large number of components, the number of possible subsets is astronomical, we cannot try to simulate all these subsets. So, the natural idea is to approximate the actual dependence of functionality on the subset by a simple expression – linear or quadratic – and to use known algorithms for optimizing such approximate expressions. In this paper, we provide an algorithm for such an approximation, and we show that for linear approximations, the resulting expression is a generalization of Shapley value – a techniques that is now successfully use to make machine-learning-based AI explainable. We also analyze how the Shapley value idea can be further improved.