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.

The goal of this paper is to establish the rate region of a wireless multi-hop, one-sender, two-receiver transmission chain. We examine and evaluate the advantages of utilizing directional antennas in this context. In particular, we consider a two-dimensional communication network with a single source node S, two destination nodes D1, D2, and 2 times (N - 1) intermediate nodes placed equidistantly between them. Multi-hop transmission is an extension of single-hop transmission that can take advantage of the reduced attenuation between closely spaced relay nodes, as well as the opportunity of spatial reuse. In two-dimensional multi-hop half-duplex transmission, each node utilizes capacity-achieving point-to-point codes to forward the most recently decoded message to its nearest neighbor in the direction of D1or D2. The transmission is performed over two parallel chains and it is a mixture of two techniques, "broadcast" communication (one transmitter to two relay nodes) and interference channel. First we describe our network and the assumptions made in the scope of this study. We further evaluate the end-to-end rate region of this topology under our transmission constraints and describe the effects that take place after replacing omni-directional antennas with perfectly directional ones. Our results indicate a 5-fold end-to-end sum rate improvement over a 10-hop network with the use of 30 degrees directional beams, as compared to omni-directional transmission.