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N prisoners locked in cells

This is fun - it opens up all kinds of fun discussion but the fact that this is done in two phases makes only one answer work. They are offered the opportunity to decide if they're going to want to ...
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4 votes

N prisoners locked in cells

There is at least one equilibrium where even with perfect knowledge of every other prisoner's strategy, no prisoner can improve their odds of survival or escape by changing strategies. At one such ...
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6 votes

N prisoners locked in cells

There is a certain paradox. If all prisoners are considered to make a perfectly logical (fixed) choice. Say that the perfect choice for the first $N-1$ prisoners contains for some of those prisoners ...
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N prisoners locked in cells

Case N=3. 1 coin appears. Prisoner 1 and prisoner 3 think "it has to be 2, because the other knows that if he puts a coin, he dies. But 2 knows that we will deduce this, so he can't have put in ...
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N prisoners locked in cells

I think that to be 100% sure everyone will put in a coin, so in the case that guessing time appears, they will say an illogical number because only they know their own cell number. That leads to a ...
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6 votes

N prisoners locked in cells

Well, cases for N=1, 2 and 3 are trivial and no need to spoiler them. prisoner gives coin, gets out. neither gives coin as the other trivially executes him. if the first or the last gave coin, second ...
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4 votes

N prisoners locked in cells

I've decide to brute-force a decision tree for $N=4$, and see if and what patterns emerge: In the outcomes, "😑" stands for "still in jail", "💀" stands for "dead&...
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N prisoners locked in cells

Let's try this, first with $N=1$ Now, what about $N=2$ ? Now for a general formula for $N$ Conclusion:
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