A hyper-rational race to 2nd place?
Five hyper-rationalists have been forced to pick a number between 1 and 100. The individual (or individuals) who pick the 2nd highest number is allowed to live, all others are executed by some capricious demon. What number do the hyper-rationalists pick and how many survive?
NB: Me and some friends spent 10 minutes discussing this and could not agree on a solution, is there one?