A guard has to persuade 5 prisoners to stay inside a circle drawn on the ground. To discourage them, he can use his one-bullet gun. To always watch them, the guard stays outside the circle. What public threat can he announce to prevent any of the prisonners from escaping?
- The prisoners are brave (they try to escape if they think they have at least one chance in a billion).
- The prisoners are not suicidal (they stay if they are 100% sure that an escape attempt will kill them).
- The prisoners know that the gun has only one bullet.
- The prisoners know each other and can communicate privately.
- The prisoners can act simultaneously and collaborate on a common strategy if: each of the collaborators staying thinks at least one prisoner will espcape, and each of the colloborators trying to escape thinks he/she has a chance.
- Most importantly, the prisoners are all rational and trust that the guard will behave in the way he announces.
A similar question has been closed as too broad and has been given an answer which is not completely satisfying. I have reformulated the question with more details about the hypothesis. Be as logical as the prisoners.