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We consider a communication system where a base station (BS) transmits updatepackets to $N$ users, one user at a time, over a wireless channel. Weinvestigate the age of this status updating system with an adversary that jamsthe update packets in the downlink. We consider two system models: withdiversity and without diversity. In the model without diversity, we show thatif the BS schedules the users with a stationary randomized policy, then theoptimal choice for the adversary is to block the user which has the lowestprobability 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 showthat for large $T$, the uniform user scheduling algorithm together with theuniform sub-carrier choosing algorithm is $\frac{2 N_{sub}}{N_{sub}-1}$optimal. Next, we investigate the game theoretic equilibrium points of thisstatus updating system. For the model without diversity, we show that a Nashequilibrium does not exist, however, a Stackelberg equilibrium exists when thescheduling algorithm of the BS acts as the leader and the adversary acts as thefollower. For the model with diversity, we show that a Nash equilibrium existsand identify the Nash equilibrium. Finally, we extend the model withoutdiversity to the case where the BS can serve multiple users and the adversarycan jam multiple users, at a time.

The Freshness Game: Timely Communications in the Presence of an Adversary