A Bilevel “Attacker-Defender” Model to Choosing the Composition of Attack Means

• Published in: Journal of applied and industrial mathematics 2019-10, Vol.13 (4), p.612-622
• Main Authors: Beresnev, V. L., Melnikov, A. A.
• Format: Article
• Language: English
• Subjects: Algorithms; Feasibility; Game theory; Integer programming; Integers; Mathematics; Mathematics and Statistics
• ISSN: 1990-4789; 1990-4797
• DOI: 10.1134/S1990478919040045

We consider a bilevel model of estimating the costs of the attacking party (the Attacker) for a successful attack of a given set of objects protected by the other party (the Defender). The Attacker and the Defender have multiple means to, correspondingly, attack and protect the objects, and the Attacker’s costs depend on the Defender’s means of protection. The model under consideration is based on the Stackelberg game, where the Attacker aims to successfully attack the objects with the least costs, while the Defender maximizes the Attacker’s losses committing some limited budget. Formally, the “Attacker—Defender” model can be written as a bilevel mixed-integer program. The particularity of the problem is that the feasibility of the upper-level solution depends on all lower-level optimal solutions. To compute an optimal solution of the bilevel problem under study, we suggest some algorithm that splits the feasible region of the problem into subsets and reducing the problem to a sequence of bilevel subproblems. Specificity of feasible regions of these subproblems allows us to reduce them to common mixed-integer programming problems of two types.