I’m not seeing what the time delays have to do with it, nor the probability distributions. Cannot they win with certainty (not just almost surely) by going to the average of all their positions?
If one person wakes up and starts to go to the center of mass, his movement will change the location of the center of mass. If another person wakes up afterwards and uses the radar, he’ll see the center of mass at a different location and this will break the coordination.
I’m not seeing what the time delays have to do with it, nor the probability distributions. Cannot they win with certainty (not just almost surely) by going to the average of all their positions?
If one person wakes up and starts to go to the center of mass, his movement will change the location of the center of mass. If another person wakes up afterwards and uses the radar, he’ll see the center of mass at a different location and this will break the coordination.
I see, that’s where the times come into it. They have no way of knowing when everyone has woken and used their radar.