  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.
