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Enlightenment of three ladies sharing money
I have a little insomnia recently. Before going to bed, I wanted to see Mr. Li Yongle talk about mathematics to promote hypnosis, but I was fascinated by his model of "giving money to three women".

The general content of this game is like this. There are three concubines A, B and C, and there are 65,438+000 gold coins. Han Feizi suggested putting forward A, B and C in order, such as A first, B second and C last. If the proposal is not passed by more than half, and more than half does not include half, the sponsor will be put to death, and the rest will continue to propose in order. If the proposal is passed, then the gold coins will be divided according to this rule. Of course, this model needs to add two assumptions. First, these three beautiful women are very smart and know how to maximize their own interests. Second, human nature is evil. If they can kill and compete for favor, they must be ruthless.

At first glance, the most embarrassing thing about this game is that A mentions it first. It must be mentioned that the last two people should be satisfied to avoid being crushed to death by the ticket. 100 block cannot be divided equally. Whoever gives more will object, but it's a dead end. But press A first. Now that A has been voted to death, only B and C are left, according to the rules, no matter what B proposes, C opposes it, which not only meets the execution conditions without more than half of the support, but even if B proposes to give all the gold coins to C, it is only for survival. According to human nature, C will also oppose getting rid of competitor B. B is well aware of his own ending after A's death, so he can only support A's proposal unconditionally in order to survive, no matter how overbearing and unreasonable A's proposal is. So looking back at A, she also understood B's situation and knew that she had B's support. No matter how C objects, it is invalid. At this time, her best proposal is that A is 100 gold, and both B and C are divided into 0.

On this basis, a king M is added. The king thinks the game is interesting and puts forward it before A. At this time, M already knows that if he is killed by a ticket, A will threaten B to get 100 gold coins, so he will choose to be good to B and C in the scheme, that is, M is 98, A is 0, B is 1, and C is 1. B and C understand that if M is killed by a ticket, they will return to the first game mode, and A will definitely take all the gold coins, but at least M gave himself 1 gold coins, so comprehensive consideration will definitely support M's proposal.

This model is idealized, a kind of gambling, and can't tolerate any anger. If B conspires with C, and finally C goes back on his word, B can't help it. But in real life, such similar games abound, and there are also many repeated operations to repair the relationship after betrayal. The lower the cost, the greater the chance of collusion.

Among them, M has the first-Mover advantage and can maximize its own interests. B and C represent low-end groups, which are easy to be suppressed and exploited, but they can also win the support of the alliance with small interests. A's position is on the mezzanine, not the object of leadership. Although ambitious, M is eyeing up and can only wait for an opportunity to turn against B and C, and then abolish M to gain the first-Mover advantage.

This model gave me a few small inspirations. First, if we must strive for the first-Mover advantage of maximum benefit, the people who make the rules can grasp the maximum profit. Second, in the position of A, on the one hand, we need to gain the trust of M, on the other hand, we need a perfect contract to contain B and C. If M is up to no good, we can unite B and C without being too passive. Finally, at the low end, don't be complacent, try to shorten the class gap, and learn to use the upper wrestling to enrich your strength for your own interests.