We introduce a game-theoretic framework for reasoning about bandwidth attacks, a common form of distributed denial of service (DDoS) attacks. In particular, our traffic injection game models the attacker as a rational but limited-resource entity who uses limited knowledge of traffic patterns to launch IP spoofing based bandwidth attacks on a server. We model the defender as a coarse-grained, relative volume based statistical filter.

We analyze the effectiveness of the defender against the attacker by analyzing the payoffs of various strategies in the traffic injection game. Furthermore, we analyze how these payoffs change in the presence of random noise.

Our results show that there is potential for using statistical methods for creating defense mechanisms that can detect a DDoS attack and that even when an attacker has a priori knowledge of the expected traffic volume for the dimension and divisions employed in the attack, the attack traffic can still be exposed to the defender.