100 how to divide the gold coins?

Five robbers robbed 100 gold coins. In order to divide the spoils, they argued endlessly, so they decided: (1) draw lots to decide everyone's number (1, 2, 3, 4, 5); (2) 1 put forward the distribution plan, and then five people voted. If more than half of the plans agree, they will pass, otherwise they will be thrown into the sea to feed sharks; (3) After the death of1,No.2 proposed a plan and four people voted. If and only if more than half agree, the plan will be passed, otherwise No.2 will also be thrown into the sea; (4) and so on, until you find a plan acceptable to everyone (of course, if there is only No.5 left, he will of course accept the result that one person takes it all). In the eyes of people who study game theory, "robber sharing money" is actually a highly simplified and abstract model (non-mathematical model), but it is undoubtedly based on reality. Assume that every robber is a "rational person" assumed by economics, who can rationally judge gains and losses and make choices. In order to avoid unnecessary disputes, we also assume that each judgment can be executed smoothly. Then, if you are the first robber, how do you propose a distribution plan to maximize your income? This question is so complicated that many people's answers are wrong. For the convenience of narration, the answer is published first and then analyzed. The first impression given by this harsh regulation is that it would be unfortunate to get the number 1. Because as the first person to come up with a plan, there is only a slim chance of survival. Even if he gave all his money to four other people, they wouldn't necessarily agree with his distribution plan, so he would only die. If you think so, the answer will go far beyond your expectation. The standard answer recognized by many people is: 1 robber gave robber No.3 1 gold coin, and two robbers No.4 or No.5 got 97 gold coins. The allocation scheme can be written as (97,0, 1, 2,0) or (97,0, 1, 0,2). As long as you don't get scared, let's analyze it from the perspective of these four people: obviously, No.5 is the most uncooperative, because he is not in danger of being thrown into the sea. Intuitively, every time he throws one, there is one less potential opponent; On the contrary, on the 4th, his chances of survival depend entirely on the fact that there is someone alive ahead, so this person seems to be worth fighting for. No.3 has no sympathy for the fate of the first two, all he needs is the support of No.3; Number two needs three votes to survive. Here I want to explain the idea of doing this problem: we should infer their decision according to strict logical thinking. The reasoning process should be from back to front, because the later the strategy, the easier it is to see. Needless to say, on the 5th, his strategy is the simplest: Babu sent everyone to feed sharks yesterday (but note: this does not mean that he has to vote against everyone, and he has to consider the passage of other people's plans). Look at No.4: If all the robbers from/kloc-0 to No.3 feed sharks, only No.4 and No.5 are left, and No.5 will definitely vote against it and let No.4 feed sharks and take all the gold coins. Therefore, No.4 can only save his life by supporting No.3. When No.3 knows this strategy, he will put forward a distribution plan (100,0,0), keep all the gold coins for himself, and don't give any money to No.4 and No.5, because he knows that No.4 got nothing, but he will still vote for it, and his plan can be passed with his own vote. However, if No.2 infers No.3' s plan, it will propose a plan of (98,0, 1, 1), that is, give up No.3 and give No.4 and No.5 1 gold coins respectively. Because the plan is more favorable to No.4 and No.5 than No.3, they will support him and don't want him to go out and be assigned by No.3 ... So No.2 took 98 gold coins. But the scheme of No.2 will be known by 1, and 1 will put forward the scheme of (97,0, 1, 2,0) or (97,0, 1, 0,2), that is, give up No.2 to No.3 65438+ because. In the mode of "robber sharing money", the key for any distributor to pass his plan is to think clearly about what the challenger's distribution plan is in advance, so as to get the maximum benefit at the least cost, thus annoying the most dissatisfied people in the challenger's distribution plan. Think about the peasant uprisings in the past dynasties, the constant struggle for the relocation of the palace, the alliance betrayal in today's life, the intrigue within the enterprise, and the mutual demolition of the government. Which winner doesn't take a method similar to "robber sharing money"? 1 It seems most likely to feed sharks, but he firmly grasped the first-Mover advantage, which not only eliminated the death threat, but also benefited the most. Isn't this the first-Mover advantage of developed countries in the process of globalization? No.5 seems to be the safest, and it can even take advantage of fishermen, but because it depends on other people's faces, it can only be divided into a small part. When you can't compete with the enemy and have no chance of winning, saving your strength is the best strategy.