Bayesian Stackelberg Game Model for Water Supply Networks against Bounded Rational Interdictors

Abstract

This work addresses how to optimize defense strategies for water supply networks against bounded rational interdictors (BRIs). BRIs may take either rational interdictions (RIs) or irrational interdictions (IIs), where RIs are strategic behavior oriented by the goal of maximizing the damage to network structure and minimizing interdiction costs, and IIs are non-strategic behavior, such as random attacks. Thus, we develop a Bayesian Stackelberg game model, where the defender initiates the game, with the objective of minimizing defense cost and minimizing the impacts on water satisfaction rate caused by either RIs or IIs, and then BRIs follow the game. In this model, since interdictions are probabilistic to be successful, BRIs hold different risk attitude to take such interdictions, which is assumed to be BRIs' private information. Besides, the probability of each component to be irrationally interdicted by BRIs is characterized based on a learning model. Then, we propose a model-based genetic algorithm to obtain the equilibriums of the Bayesian Stackelberg game model. The case study of D-Town water network demonstrates the practical applicability and discuss how to defend water supply networks against BRIs.