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"当只有2、3、4、5四个人时，2提出的任何方案3都不会同意", this is right. But for 5, he knows that if it comes to the situation "当只有3、4、5三个人时", 3 can only will give him 0 since "4为了保全自己，不管3提出什么样的方案都会同意". And 3 only need one more person to agree. 3 can only give 5 nothing. So "当只有2、3、4、5四个人时", if 2 offer 5 one diamond, then he will totally accept this plan.
"当只有2、3、4、5四个人时", For 2, he need 2 additional tickets. he knows what 5's thought cause he is clever. so he will give 5 one diamond. He also will give 4 one diamond and 4 will accept it for sure. Because if 2 dies, it comes to the situation of "当只有3、4、5三个人时，4为了保全自己，不管3提出什么样的方案都会同意". In this case, 3 can give 4 nothing. One diamond is better than nothing. So 4 will accept this offer by 2.
After the analysis, "当只有2、3、4、5四个人时，2提出 98,0,1,1 and he will get two tickets from 4 and 5.
both 1 and 2 are clever enough to know this situation. So 2 will reject any offer by 1(Since he can get 98 otherwise). so 1 have to get 2 more ticket from 3,4,5. He give 3 one diamond, and he bet 3 will accept it. Think about if "当只有2、3、4、5四个人时", he will get nothing from 2.
1 also will choose one more ticket from 4 or 5. Since "当只有2、3、4、5四个人时" 4 and 5 each get 1 diamond. 1 can give 4 or 5 two diamonds, any of them will accept this plan, since it's better than the offer 2 can give.
So the final offer by 1 is: 97,0,1,2,0 or 97,0,1,0,2
He will win 3 tickets to agree. |
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