Conditions:
1 because only more than half of the people agree to the distribution, that is to say, if less than half of the people agree, the person who puts forward the distribution plan will definitely die.
The benefits of distribution are: life >; Gem > the pleasure of killing your partner
Analysis:
1 For No.5, he is immortal, so his advantage lies in the gem and the pleasure of killing his partner;
For No.4, according to the rules, he will never tolerate his turn to distribute, so as long as No.3 distributes, no matter how No.3 distributes, he will agree;
Rational No.5 will know what No.4 thinks, and at the same time know that if it is No.3' s turn to allocate, then he and No.4 will have nothing. Therefore, No.5 will vote before the 3rd round, because the advantage of No.5 is a gem >: the pleasure of killing his partner, so no matter whether 1 or No.2 is assigned to him, as long as he gives the gem, he may agree (this is possible, because No.5 must choose whether 1 gives himself more gems or No.2 makes himself more gems), otherwise he will choose negative opinions to get the potential pleasure of killing his partner.
Rational No.4 certainly knows No.5' s voting strategy, and at the same time understands that No.3 makes his own fortune, so his strategy is 1 or whether No.2 can give himself a gem.
Rational No.2 will know the voting strategies of No.4 and No.5 very well, so as long as it is his turn to allocate, he can give No.4 and No.5 the lowest 1 gem, and they will also agree with themselves. And if one person is missing for the GEM, then that person will vote against it, and No.3 also knows the situation, so he will also deny it, so there will be no blessing to enjoy the GEM. Therefore, No.2 must give No.4 and No.5 1 gems when it is his turn to distribute them.
6 Rationality 1 Of course, I know the ideas of No.2, No.3, No.4 and No.5, and 1 this number only needs to attract two people to vote for it at the minimum cost. Because if the allocation scheme of No.2 is adopted, No.2 only needs two GEM costs to succeed, then the cost of 1 will be greater than or equal to two. Assuming the cost is 2, there are (2,3) (2,4) (2,5) (3,4) (3,5) (4,5) distribution combinations. Obviously, there will be more than three negative votes in these combinations, so the minimum cost is not 2. Suppose the lowest cost is 3. If the lowest cost is shared equally by three people, the possible combination is (2, 3, 4)(2, 3, 5)(2, 4, 5)(3, 4, 5). Obviously, none of them will work. Suppose it is not for three people, but for two people, one with two gems and one with 1 gem. Obviously, all the combinations given to No.2 are excluded, because if No.2, No.4 and No.5 are given, one of them will have no gems, while the other one will have at most 1 gems, which is the same as the distribution of No.2, but killing 1 will be very pleasant, so it is certain. Therefore, the allocation scheme can only be selected between No.3, No.4 and No.5. Assuming that No.3 is not selected, No.3 will definitely oppose it to obtain the possibility of potentially killing 1, so No.2 and No.3 will oppose it, while the remaining No.4 and No.5 will obtain the same benefits as No.2, so they will definitely oppose it to obtain the pleasure of killing 1, so it is necessary to allocate No.3 gem to obtain it. And the remaining 4, 5 because you need to give more gems than allocation 2 can give. Therefore, the distribution scheme of 1 is the No.3 1 gem at the expense of No.3, and the two gems of No.4 or No.5 will definitely get two affirmative votes.
So the allocation scheme is: 97; 0; 1; 0; 2 or 97; 0; 1; 2; 0
In fact, this problem can also be solved mathematically, but it is necessary to list the benefits through a tree diagram (for example, the loss of life is-1, the value of n gems is n, the pleasure of killing an accomplice is A, and the field of this A is 0.
The whole allocation process is allocated to one step according to the round of an island.
Step 1: Let the distribution scheme of 1 be (n 1, n2, n3, n4, n5), n1+N2+n3+n4+n5 =100, and ni belongs to n. When agreed, all parties will benefit (n 1, n2, n3, n4, n5). In case of disagreement, 1 dies and enters step2, where it is distributed by No.2, and all parties benefit (-1, step2).
Step 2: Formulate the No.2 allocation scheme (n2', n3', n4', n5'). Similarly, this step is divided into binary trees. ...
……
Step five
Then calculate, you can solve:
N 1 = 97, N2 = 0, N3 = 1, (N4 = 2, N5 = 0) or (N4 = 0, N5 = 2).