Hypothesis testing game for cyber deception

Deception is a technique to mislead human or computer systems by manipulating beliefs and information. Successful deception is characterized by the information-asymmetric, dynamic, and strategic behaviors of the deceiver and the deceivee. This paper proposes a game-theoretic framework to capture these features of deception in which the deceiver sends the strategically manipulated information to the deceivee while the deceivee makes the best-effort decisions based on the information received and his belief. In particular, we consider the case when the deceivee adopts hypothesis testing to make binary decisions and the asymmetric information is modeled using a signaling game where the deceiver is a privately-informed player called sender and the deceivee is an uninformed player called receiver. We characterize perfect Bayesian Nash equilibrium (PBNE) solution of the game and study the deceivability of the game. Our results show that the hypothesis testing game admits pooling and partially-separating-pooling equilibria. In pooling equilibria, the deceivability depends on the true types, while in partially-separating-pooling equilibria, the deceivability depends on the cost of the deceiver. We introduce the receiver operating characteristic curve to visualize the equilibrium behavior of the deceiver and the performance of the decision making, thereby characterizing the deceivability of the hypothesis testing game.