I guess the unstated assumption is that the prisoners can only see the temperatures of others from the previous round and/or can only change their temperature at the start of a round (though one tried to do otherwise in the story). Even with that it seems like an awfully precarious equilibrium since if I unilaterally start choosing 30 repeatedly, you’d have to be stupid to not also start choosing 30, and the cost to me is really quite tiny even while no one else ever ‘defects’ alongside me. It seems to be too weak a definition of ‘equilibrium’ if it’s that easy to break—maybe there’s a more realistic definition that excludes this case?
The other thing that could happen is silent deviations, where some players aren’t doing “punish any defection from 99”—they are just doing “play 99″ to avoid punishments. The one brave soul doesn’t know how many of each there are, but can find out when they suddenly go for 30.
I guess the unstated assumption is that the prisoners can only see the temperatures of others from the previous round and/or can only change their temperature at the start of a round (though one tried to do otherwise in the story). Even with that it seems like an awfully precarious equilibrium since if I unilaterally start choosing 30 repeatedly, you’d have to be stupid to not also start choosing 30, and the cost to me is really quite tiny even while no one else ever ‘defects’ alongside me. It seems to be too weak a definition of ‘equilibrium’ if it’s that easy to break—maybe there’s a more realistic definition that excludes this case?
The other thing that could happen is silent deviations, where some players aren’t doing “punish any defection from 99”—they are just doing “play 99″ to avoid punishments. The one brave soul doesn’t know how many of each there are, but can find out when they suddenly go for 30.