Solve the below:
Q: Two agents play the hide-and-seek game in sev- eral rooms with different illumination levels. Agent 1 hides himself in a room, while agent 2 has to choose the room to seek for him. Illumination levels of all rooms are common knowledge. The agents use the following strategies. Under the remaining equal condi- tions, the seeker prefers to seek in the rooms having a higher illumination level (finding the hider is easier).
The hider understands that the seeker has little chance of success in a room with a lower illumination level. The growing rank of reflexion means that an agent understands that this fact is clear to his or her oppo- nent and so on. What are the maximal rational ranks of reflexion for the agents?