Efficient Communication for Pursuit-Evasion Games with Asymmetric Information

We consider a class of pursuit-evasion differential games in which the evader has continuous access to the pursuer's location, but not vice-versa. There is an immobile sensor (e.g., a ground radar station) that can sense the evader's location and communicate that information intermittently to the pursuer. Transmitting the information from the sensor to the pursuer is costly and only a finite number of transmissions can happen throughout the entire game. The outcome of the game is determined by the control strategies of the players and the communication strategy between the sensor and the pursuer. We obtain the (Nash) equilibrium control strategies for both the players as well as the optimal communication strategy between the static sensor and the pursuer. We discuss a dilemma for the evader that emerges in this game. We also discuss the emergence of implicit communication where the absence of communication from the sensor can also convey some actionable information to the pursuer.