Detection games with a fully active attacker

We analyze a binary hypothesis testing problem in which a defender has to decide whether or not a test sequence has been drawn from a given source P0 whereas, an attacker strives to impede the correct detection. In contrast to previous works, the adversarial setup addressed in this paper considers a fully active attacker, i.e. the attacker is active under both hypotheses. Specifically, the goal of the attacker is to distort the given sequence, no matter whether it has emerged from P0 or not, to confuse the defender and induce a wrong decision. We formulate the defender-attacker interaction as a game and study two versions of the game, corresponding to two different setups: a Neyman-Pearson setup and a Bayesian one. By focusing on asymptotic versions of the games, we show that there exists an attacking strategy that is both dominant (i.e., optimal no matter what the defence strategy is) and universal (i.e., independent of the underlying sources) and we derive equilibrium strategies for both parties.