Abstract. Consider the following game between a worm and an alert 3 over a network of n nodes. Initially, no nodes are infected or alerted and each node in the network is a special detector node independently with small but constant probability. The game starts with a single node becoming infected. In every round thereafter, every infected node sends out a constant number of worms to other nodes in the population, and every alerted node sends out a constant number of alerts. Nodes in the network change state according to the following four rules: 1) If a worm is received by a node that is not a detector and is not alerted, that node becomes infected; 2) If a worm is received by a node that is a detector, that node becomes alerted; 3) If an alert is received by a node that is not infected, that node becomes alerted; 4) If a worm or an alert is received by a node that is already infected or already alerted, then there is no change in the state of that node. We make two assumptions about this game. First, that an infected nod
