Another application of game theory is also related to security. In this case, instead of multiple but all identical nodes, we can focus on just two players but of different kinds: one legitimate transmitter and one attacker. In this case the attacker wants to destroy the activity of the transmitter. For example, if the latter is a wireless sensor in a cyber-physical system, the attacker wants to prevent the network intelligence from making accurate decision-making, which can be done by poisoning the information about the system state. The lack of fresh and accurate information about the system state is usually quantified through a metric called age of incorrect information (AoII). Thus, we consider a security scenario where an adversary may inject false data to make the information available at the network controller incorrect, which can only be contrasted by additional measurements. This results in a game played by strategic agents, for which we provide an equilibrium analysis and discuss the role of different system parameters. In particular, we show how this enables us to determine a threshold behavior for the attacker, which is active only if its cost is below a certain threshold. This can be seen as a security criterion, that is, how much the transmitter should increase the cost paid by an adversary to avoid being attacked.