Building A Mathematical Model for Allocation Problem of an Attack-Defense Game

In the attack defense game, the attacker (player1) moves and allocates his resources (targets) to attack valuable assets for the defender, then the defender (player2) moves and allocates his resources (killing elements) to protect his defended assets. The task of the defender to allocate his killing elements is not far from to be trivial. A functional overview of the defender’s decision support system will be shown in this work. Once the threat value for each target (resources of player1) has been estimated by the defender’s decision support system, the defender’s allocation problems appear. In this paper, a bi-objective model for the defender’s allocation problem is proposed. The first objective is to minimize the estimated total value of surviving targets and the second objective is to minimize the cost of the defender’s killing elements. The important features of the proposed model are:•Using the method of weights to identify a set of nondominated (efficient) solutions for the defender’s allocation problem.•It helps the decision maker to interact with the allocation problem by varying the weights until getting a suitable solution from his point of view.A numerical example is presented in this paper to show that the single objective model is a special case of the proposed bi-objective one.