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一位无防卫力量的游客到了沙漠，被一群食人者包围。食人者吃了游客后会变弱，容易被其它吃人者吃掉。食人者都肌饿并且都不互信会合作。请问离这游客最近的食人者会吃掉人吗？
食人者数量n=1时，毫无疑问食人者吃掉这个游客；
食人者数量n=2时，两个食人者都不会吃掉这个游客。因为任一食人者吃掉游客后都会被另一个食人者吃掉。
食人者数量n=3时，离游客最近的食人者吃掉这个游客，吃掉游客后这个食人者变弱，我们把它看成是游客，因此变成一个游客和两个食人者的问题。
下面是原文：
The world of cannibalism.
Here's the problem:
A traveler gets lost on a deserted island and finds himself surrounded by a group of n cannibals.
Each cannibal wants to eat the traveler but, as each knows, there is a risk. A cannibal that attacks and eats the traveler would become tired and defenseless. After he eats, he would become an easy target for another cannibal (who would also become tired and defenseless after eating).
The cannibals are all hungry, but they cannot trust each other to cooperate. The cannibals happen to be well versed in game theory, so they will think before making a move.
Does the nearest cannibal, or any cannibal in the group, devour the lost traveler?
The first step is to recognize that the traveler is just a tired and defenseless cannibal. Once you do that, the problem can be reduced to one just involving cannibals. To solve it now, let's take small sample sizes.
Sample Size: n = 1
This is almost a laughably easy problem to solve. If there's one cannibal, and of course the one traveler, then the cannibal will obviously eat the traveler, as he has nothing to fear from any other cannibals.
Sample Size: n = 2
Two hungry cannibals and a defenseless traveler makes for a harder problem. Remember that we concluded that the traveler is effectively a defenseless cannibal, and by extension a defenseless cannibal is merely a traveler.
What the cannibals will probably realize that if one of them eats the traveler, they will become prey for the other cannibal. Therefore, their eating the traveler constitutes their death.
Because of this, neither cannibal will attack and the traveler will be safe.
Sample Size: n = 3
Here's where the problem gets interesting.
If there are three cannibals and one traveler, this problem can be reduced to one that we have solved before. Assuming that the cannibals are well versed in game theory, they will figure out that the first one to attack will reap the benefits.
What do I mean when I say that? If one cannibal eats the traveler, they become a traveler, and the problem is reduced to n = 2. Therefore, the remaining two cannibals will not attack, and the first cannibal to attack will be safe.
How do we solve this problem, then? If there are an odd number of cannibals, the cannibals will attack; Given an even number of cannibals, they will not attack and the traveler will be safe.
This is not a pure game theory problem, but it certainly is an interesting, attention-grabbing example.. Hope this helps!
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