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.

翻译：研究一类追逃微分博弈问题，其中逃逸者能够持续获取追踪者的位置信息，反之则不然。存在一个固定传感器（如地面雷达站）可感知逃逸者位置，并间歇性地将该信息传递给追踪者。从传感器到追踪者的信息传输具有成本，且整个博弈过程中仅允许有限次数的传输。博弈结果由双方控制策略以及传感器与追踪者之间的通信策略共同决定。本文推导了双方玩家的（纳什）均衡控制策略，并确定了静态传感器与追踪者之间的最优通信策略。同时探讨了逃逸者在博弈中面临的困境，并分析了隐含通信现象——即传感器未发送通信信号本身也可能向追踪者传递可行动信息。