  In this work, we introduce and study the \emph{$(\alpha, \beta)$-Monitoring}
game on networks. Our game is composed of two parties an attacker and a
defender. The attacker can launch an attack by distributing a limited number of
seeds (i.e., virus) to the network, and/or manipulate the propagation
probabilities on a limited number of edges. Under our $(\alpha,
\beta)$-Monitoring game, we say an attack is successful if and only if the
following two conditions are satisfied: (1) the outbreak/propagation reaches
$\alpha$ individuals, and (2) it has not been detected before reaching $\beta$
individuals. On the other end, the defender's ultimate goal is to deploy a set
of monitors in the network that can minimize attacker's success ratio in the
worst-case. Our work is built upon recent work in security games, compared with
stochastic guarantees, our adversarial setting leads to more robust solutions
in practice.
