  Strategic interactions ranging from politics and pharmaceuticals to
e-commerce and social networks support equilibria in which agents with private
information manipulate others which are vulnerable to deception. Especially in
cyberspace and the Internet of things, deception is difficult to detect and
trust is complicated to establish. For this reason, effective policy-making,
profitable entrepreneurship, and optimal technological design demand
quantitative models of deception. In this paper, we use game theory to model
specifically one-to-many deception. We combine a signaling game with a model
called a Poisson game. The resulting Poisson signaling game extends traditional
signaling games to include 1) exogenous evidence of deception, 2) an unknown
number of receivers, and 3) receivers of multiple types. We find closed-form
equilibrium solutions for a subset of Poisson signaling games, and characterize
the rates of deception that they support. We show that receivers with higher
abilities to detect deception can use crowd-defense tactics to mitigate
deception for receivers with lower abilities to detect deception. Finally, we
discuss how Poisson signaling games could be used to defend against the process
by which the Mirai botnet recruits IoT devices in preparation for a distributed
denial-of-service attack.
