Protecting Infrastructure Networks: Solving the Stackelberg Game with Interval-Valued Intuitionistic Fuzzy Number Payoffs

Yibo Dong, Jin Liu, Jiaqi Ren, Zhe Li and Weili Li ()
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Yibo Dong: Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha 410073, China
Jin Liu: Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha 410073, China
Jiaqi Ren: Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha 410073, China
Zhe Li: Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha 410073, China
Weili Li: Science and Technology on Information Systems Engineering Laboratory, National University of Defense Technology, Changsha 410073, China

Mathematics, 2023, vol. 11, issue 24, 1-18

Abstract: Critical infrastructure is essential for the stability and development of modern society, and a combination of complex network theory and game theory has become a new research direction in the field of infrastructure protection. However, existing studies do not consider the fuzziness and subjective factors of human judgment, leading to challenges when analyzing strategic interactions between decision makers. This paper employs interval-valued intuitionistic fuzzy numbers (IVIFN) to depict the uncertain payoffs in a Stackelberg game of infrastructure networks and then proposes an algorithm to solve it. First, we construct IVIFN payoffs by considering the different complex network metrics and subjective preferences of decision makers. Next, we propose a lexicographic algorithm to solve this game based on the concept of a strong Stackelberg equilibrium (SSE). Finally, we conduct experiments on target scale-free networks. Our results illustrate that in an SSE, for the defender in a weak position, it is better to defend nodes with high degrees. The experiments also indicate that taking fuzziness into account leads to higher SSE payoffs for the defender. Our work aims to solve a Stackelberg game with IVIFN payoffs and apply it to enhance the protection of infrastructure networks, thereby improving their overall security.

Keywords: infrastructure networks; Stackelberg game; interval-valued intuitionistic fuzzy theory; strong Stackelberg equilibrium (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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