Attack detection is usually approached as a classification problem. However, standard classification tools often perform poorly, because an adaptive attacker can shape his attacks in response to the algorithm. This has led to the recent interest in developing methods for adversarial classification, but to the best of our knowledge, there have been a very few prior studies that take into account the attacker's tradeoff between adapting to the classifier being used against him with his desire to maintain the efficacy of his attack. Including this effect is a key to derive solutions that perform well in practice. In this investigation, we model the interaction as a game between a defender who chooses a classifier to distinguish between attacks and normal behavior based on a set of observed features and an attacker who chooses his attack features (class 1 data). Normal behavior (class 0 data) is random and exogenous. The attacker's objective balances the benefit from attacks and the cost of being detected while the defender's objective balances the benefit of a correct attack detection and the cost of false alarm. We provide an efficient algorithm to compute all Nash equilibria and a compact characterization of the possible forms of a Nash equilibrium that reveals intuitive messages on how to perform classification in the presence of an attacker. We also explore qualitatively and quantitatively the impact of the non-attacker and underlying parameters on the equilibrium strategies.

Mobile data traffic has been steadily rising in the past years. This has generated a significant interest in the deployment of incentive mechanisms to reduce peak-time congestion. Typically, the design of these mechanisms requires information about user demand and sensitivity to prices. Such information is naturally imperfect. In this paper, we propose a fixed-budget rebate mechanism that gives each user a reward proportional to his percentage contribution to the aggregate reduction in peak-time demand. For comparison, we also study a time-of-day pricing mechanism that gives each user a fixed reward per unit reduction of his peak-time demand. To evaluate the two mechanisms, we introduce a game-theoretic model that captures the public good nature of decongestion. For each mechanism, we demonstrate that the socially optimal level of decongestion is achievable for a specific choice of the mechanism's parameter. We then investigate how imperfect information about user demand affects the mechanisms' effectiveness. From our results, the fixed-budget rebate pricing is more robust when the users' sensitivity to congestion is “sufficiently” convex. This feature of the fixed-budget rebate mechanism is attractive for many situations of interest and is driven by its closed-loop property, i.e., the unit reward decreases as the peak-time demand decreases.

We study a simple ingress policing scheme for a stochastic queuing network that uses a round-robin service discipline, and derive conditions under which the flow rates approach a max-min fair share allocation. The scheme works as follows: Whenever any of a flow's queues exceeds a policing threshold, the network discards that flow's arriving packets at the network ingress, and does so until all of that flow's queues fall below their thresholds. To prove our results, we use previously known results relating the stability of a queuing system to the stability of its fluid limit and extend these results to relate the flow rates of the stochastic system to those of a corresponding fluid model. In particular, we consider the fluid limit of a sequence of queuing networks with increasing thresholds. Using a Lyapunov function derived from the fluid limits, we find that as the policing thresholds are increased the state of the stochastic system is attracted to a relatively smaller and smaller neighborhood surrounding the equilibrium of the fluid model. We then show how this property implies that the achieved flow rates approach the max-min rates predicted by the fluid model.