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 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 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.
Abstract Starting with the analysis of arms control and disarmament problems in the sixties, inspection games have evolved into a special area of game theory with specific theoretical aspects, and, equally important, practical applications in various fields of human activity where inspection is mandatory. In this contribution, a survey of applications is given first. These include arms control and disarmament, theoretical approaches to auditing and accounting, for example in insurance, and problems of environmental surveillance. Then, the general problem of inspection is presented in a game-theoretic framework that extends a statistical hypothesis testing problem. This defines a game since the data can be strategically manipulated by an inspectee who wants to conceal illegal actions. Using this framework, two models are solved, which are practically significant and technically interesting: material accountancy and data verification. A second important aspect of inspection games is the fact that inspection resources are limited and have to be used strategically. This is demonstrated in the context of sequential inspection games, where many mathematically challenging models have been studied. Finally, the important concept of leadership, where the inspector becomes a leader by announcing and committing himself to his strategy, is shown to apply naturally to inspection games. Abstract : Many disarmament or arms-control agreements may be monitored by sample inspections. Unlike the usual sampling procedures, sampling for arms-control agreements must take into account the possibility that the statistical universe from which samples are to be drawn may be tampered with so as to decrease the probability of detection of a violation. A game-theoretic model is formulated for studying a sampling problem in which the inspector is allowed to examine a fixed number (usually small) of items or natural events (e.g., items from an assembly line under an agreement limiting military production, or seismic events under a nuclear test-ban agreement). It is assumed that the inspections are to be performed within a fixed time period or on a series of events of fixed length. Optimal sampling procedures are derived as functions of the number of inspections and the size of the statistical universe. Some variations on the model are briefly considered. Abstract : An inspector's game is a non-constant sum 2person game in which one player has promised to perform a certain duty a5d the other player is allowed to occasionally inspect and verify that the duty has indeed been performed. A solution to a variant of such a game is given in this paper, based on the assumption that the inspector can announce his mixed strategy in advance, if he so wishes, whereas the other player, who has already given his promise, cannot threat by explicitly saying that he will not keep his word. (Author)