Multi-objective Stackelberg game model for water supply networks against interdictions with incomplete information

Water supply networks are infrastructures pivotal to economic development and living standards, of which the increasing complexity and interdependencies have brought challenges for the protection and enhancement of water supplies. We address the problem on how to defend water supply networks with hydraulic characteristics against an interdictor by building a multi-objective Stackelberg game model with incomplete information. In this model, the defender and the interdictor, both considered as rational players, choose a subset of network components to defend or interdict based on their payoffs. The defender, with incomplete information on the interdictor's efforts, initiates to trade off the two objectives of maximizing the expected network satisfaction rate and of minimizing defense efforts, whereas the interdictor, with no information on network operational capacity, follows to trade off the objectives of minimizing the expected network efficiency and of minimizing interdiction efforts. The algorithm of determining the final optimal defense strategies is presented, which consists of three steps: (1) develop the strategy sets by the assessments of network vulnerability and resilience; (2) analyze the equilibrium through a nested heuristic genetic algorithm; and (3) determine the final optimal defense strategy based on the minimax regret approach. A case study of D-town water supply network demonstrates the practical significance of the proposed approach. Furthermore, the impacts of the incomplete information are analyzed to provide suggestions on the defense strategy making.