Five pirates got 100 gold coins, and they decided the distribution order according to the lottery: pirates 1 first made the distribution, and if his distribution result was recognized by half or more pirates, it was carried out according to his distribution result. Otherwise, he will be thrown into the sea to feed sharks, then distributed by Viking II, and so on. So how does Pirate One ensure the maximization of its own interests?
Of course, there are two basic assumptions:
1. First of all, it is required that the allocation and implementation must be carried out in strict accordance with the rules.
2. Secondly, all pirates are required to be completely rational, that is to say, they will not joke about their own lives and gamble for uncertain interests. Will ensure their most secure income.
Here are a few words, and interested readers can think about the solution to this problem by themselves. See if you can come up with a reasonable explanation.
There is also a passage in "Nine Songs" in which the problem of "three queens sharing money" explained by Han Fei appears, which is essentially a problem of sharing money with pirates. This will soon be formalized in the following explanation.
Interrupt end
Next, let's look at the solution to this problem: it doesn't seem easy to solve it directly. So we can use backward induction. Start with a pirate and then go back.
A pirate
When there is only one pirate left, he will definitely keep all the gold coins for himself, so the result is: 100.
Two pirates
When there are two pirates left, only pirate No.2 needs his own consent, and the number will reach half. So he doesn't have to consider the number 1, and directly allocates: 01001002100.
Three pirates
When there are three pirates left, No.2 will certainly not support No.3' s plan, because as long as No.3 is thrown down, No.2 can keep the gold coins for himself.
Then No.3 must win the support of 1 and pay more than 0 gold coins of 1. 1 is enough. So the distribution result at this time is 1 0 99, that is, 1No. 1 No.2, No.0 3,99.
At this time, it is the answer to the problem of sharing money among the three singers in "Song of Nine Days". As a result, the first singer can get 99.
Four pirates
Similarly, when distributing Pirate 4, it is inevitable that you will not spend a lot of money to seek the support of Pirate 3, but invest in Pirate 2 and choose to win over. The result is 0 1 0 99.
Five pirates
Similarly, the result of five pirates is 1 0 1 0 98. This is the answer to the problem that five pirates share gold coins.
To put it simply, when everyone is absolutely rational, it is better to start first and then suffer.
On the issue of sharing money among pirates, it doesn't stop there. Interested readers can search for more content by themselves. This paper puts an economic case in the collection of Mathematical Culture. Just introduce the mathematical thought of "backward induction". Great things in the world must be done in detail, and difficult things in the world must be done easily. When we are not sure about a thing or a difficult problem, we might as well trace back to the source, start with a simple model and analyze it step by step to get the desired result. I think this is the essence of induction.