  We consider a communication system where a base station (BS) transmits update
packets to $N$ users, one user at a time, over a wireless channel. We
investigate the age of this status updating system with an adversary that jams
the update packets in the downlink. We consider two system models: with
diversity and without diversity. In the model without diversity, we show that
if the BS schedules the users with a stationary randomized policy, then the
optimal choice for the adversary is to block the user which has the lowest
probability of getting scheduled by the BS, at the middle of the time horizon,
consecutively for $\alpha T$ time slots. In the model with diversity, we show
that for large $T$, the uniform user scheduling algorithm together with the
uniform sub-carrier choosing algorithm is $\frac{2 N_{sub}}{N_{sub}-1}$
optimal. Next, we investigate the game theoretic equilibrium points of this
status updating system. For the model without diversity, we show that a Nash
equilibrium does not exist, however, a Stackelberg equilibrium exists when the
scheduling algorithm of the BS acts as the leader and the adversary acts as the
follower. For the model with diversity, we show that a Nash equilibrium exists
and identify the Nash equilibrium. Finally, we extend the model without
diversity to the case where the BS can serve multiple users and the adversary
can jam multiple users, at a time.
