Modeling and Analysis of Leaky Deception using Signaling Games with Evidence

Deception plays critical roles in economics and technology, especially in emerging interactions in cyberspace. Holistic models of deception are needed in order to analyze interactions and to design mechanisms that improve them. Game theory provides such models. In particular, existing work models deception using signaling games. But signaling games inherently model deception that is undetectable. In this paper, we extend signaling games by including a detector that gives off probabilistic warnings when the sender acts deceptively. Then we derive pooling and partially-separating equilibria of the game. We find that 1) high-quality detectors eliminate some pure-strategy equilibria, 2) detectors with high true-positive rates encourage more honest signaling than detectors with low false-positive rates, 3) receivers obtain optimal outcomes for equal-error-rate detectors, and 4) surprisingly, deceptive senders sometimes benefit from highly accurate deception detectors. We illustrate these results with an application to defensive deception for network security. Our results provide a quantitative and rigorous analysis of the fundamental aspects of detectable deception.