Imbalanced Collusive Security Games

Colluding adversaries is a crucial challenge for defenders in many real-world applications. Previous literature has provided Collusive Security Games (COSG) to model colluding adversaries, and provided models and algorithms to generate defender strategies to counter colluding adversaries, often by devising strategies that inhibit collusion [6]. Unfortunately, this previous work focused exclusively on situations with perfectly matched adversaries, i.e., where their rewards were symmetrically distributed. In the real world, however, defenders often face adversaries where their rewards are asymmetrically distributed. Such inherent asymmetry raises a question as to whether human adversaries would attempt to collude in such situations, and whether defender strategies to counter such collusion should focus on inhibiting collusion. To address these open questions, this paper: (i) explores and theoretically analyzes Imbalanced Collusive Security Games (ICOSG) where defenders face adversaries with asymmetrically distributed rewards; (ii) conducts extensive experiments of three different adversary models involving 1800 real human subjects and (iii) derives novel analysis of the reason behind why bounded rational attackers models outperform perfectly rational attackers models. The key principle discovered as the result of our experiments is that: careful modeling of human bounded rationality reveals a key difference (when compared to a model using perfect rationality) in defender strategies for handling colluding adversaries which face symmetric vs asymmetric rewards. Whereas a model based on perfect rationality always attempts to break collusion among adversaries, a bounded rationality model acknowledges the inherent difficulty of breaking such collusion in symmetric situations and focuses only on breaking collusion in asymmetric situation, and only on damage control from collusion in the symmetric situation.