A Zero-Sum Game of Age of Information Over a Finite Horizon Between Sensor and Adversary

We analyze the interplay between a sensor reporting real-time data and an adversary that wants to disrupt communication, modeled as a strategic agents in a zero-sum game. The value of the game is set as age of information (AoI) over a finite horizon, over which the sensor sends n reporting milestones as equally-spaced update instants. The adversary can choose to jam some of these milestones, while at the same time the sensor can adopt a defense mechanism (i.e., to increase the transmission power) also on a limited number of milestones, to protect them from the adversary’s jamming. This implies that the adversary chooses the milestones to jam trying to circumvent the sensor’s defenses, whereas the sensor wants to choose the same transmission instants as the adversary so as to prevent its jamming. These choices are performed in a simultaneous-move game, i.e., without knowledge of the opponent’s choice, and the resulting AoI is computed. We discuss the value of the game at the Nash equilibrium, and the impact of the strategic degrees of freedom of the players.