Defensive resource allocation in terrorism conflict management based on graph model with relative preferences

In real-world counterterrorism activities, it is usually difficult for the defender and the attacker to accurately know the private information of the each other such as valuations of targets. Instead, players may only know the relative preference on the target valuations from the adversary. In the conflict analysis, graph model is a powerful tool for dealing with relative preferences. This paper studies the defensive resource allocation in terrorism conflict management with incomplete information by establishing a graph model. To solve the model, we divide the conflict states into two types and discuss the conditions under which these two types of states are at equilibrium. Furthermore, we study how the defender should optimally allocate the resource to achieve two goals: (i) achieving a certain Nash equilibrium state desired by the defender; and (ii) minimizing the total loss from an attack in equilibrium. Subsequently, we conduct several numerical analyses: (i) analyzing the effects of both players' investment effectiveness on the optimal defense loss; (ii) comparing our model's results with those obtained using three classical decision methods, revealing that the defense loss in our model is lower; and (iii) presenting a case study to illustrate the applicability of the proposed model. This paper provides novel insights on how to efficiently allocate defensive resource when the defender and attacker know only the relative preference of the adversary on target valuations.