Bi-level programming for modeling a multi-target attacker-defender game with budget allocation constraint and solving it using a neural network approach

Effective allocation of the defense budget is one of the important duties of governments in the fight against terrorism. In this paper, using the bi-level optimization and the sequential-move game, we introduce a new multi-target attacker-defender game with budget constraints to model the strategic interactions between attacker (terrorists) and defender (governments). We focus on the different types of attacks adopted by the attacker. Using the Karush-Kuhn-Tucker optimality conditions, the proposed bi-level programming problem is reduced to a one-level mathematical program with complementarity constraints. We then design a capable neural network to solve this one-level mathematical programming problem by using the perturbed Fischer-Burmeister function, optimization theory, and some concepts of ordinary differential equations. It is shown that the proposed neural network is asymptotic stable and convergent to the optimal solution of the bi-level programming problem. Finally, we show the performance and validity of the proposed method by using two scenarios.