While the Internet of things (IoT) promises to improve areas such as energy efficiency, health care, and transportation, it is highly vulnerable to cyberattacks. In particular, distributed denial-of-service (DDoS) attacks overload the bandwidth of a server. But many IoT devices form part of cyber-physical systems (CPS). Therefore, they can be used to launch "physical" denial-of-service attacks (PDoS) in which IoT devices overflow the "physical bandwidth" of a CPS. In this paper, we quantify the population-based risk to a group of IoT devices targeted by malware for a PDoS attack. In order to model the recruitment of bots, we develop a "Poisson signaling game," a signaling game with an unknown number of receivers, which have varying abilities to detect deception. Then we use a version of this game to analyze two mechanisms (legal and economic) to deter botnet recruitment. Equilibrium results indicate that 1) defenders can bound botnet activity, and 2) legislating a minimum level of security has only a limited effect, while incentivizing active defense can decrease botnet activity arbitrarily. This work provides a quantitative foundation for proactive PDoS defense.