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Game Theoretic Analysis of an Adversarial Status Updating System

We investigate the game theoretic equilibrium points of a status updating system with an adversary that jams the updates in the downlink. We consider the system models with and without diversity. The adversary can jam up to $α$ proportion of the entire communication window. In the model without diversity, in each time slot, the base station schedules a user from $N$ users according to a stationary distribution. The adversary blocks (jams) $αT$ time slots of its choosing out of the total $T$ time slots. For this system, we show that a Nash equilibrium does not exist, however, a Stackelberg equilibrium exists when the scheduling algorithm of the base station acts as the leader and the adversary acts as the follower. In the model with diversity, in each time slot, the base station schedules a user from $N$ users and chooses a sub-carrier from $N_{sub}$ sub-carriers to transmit update packets to the scheduled user according to a stationary distribution. The adversary blocks $αT$ time slots of its choosing out of $T$ time slots at the sub-carriers of its choosing. For this system, we show that a Nash equilibrium exists and identify the Nash equilibrium.