Lead:

It is said that 5 robbers robbed 100 gold coins, and the way everyone decided to divide the spoils was: first the most ferocious pirate proposed a distribution plan, and then everyone voted on one person, and if 50% or more of the pirates agreed to this plan, then they would be distributed according to this plan; If less than 50% of the pirates agree, then the pirate who proposed the plan will be thrown out into the sea to feed the fish, and then the most vicious of the remaining pirates will come up with the plan, and so on. Let's assume that these pirates are extremely clever and don't cooperate with each other, and that each pirate wants to get as much gold as possible. So, how will the first proposed pirate propose to get the proposal through and maximize the amount of gold?

Pirates are a group of outlaws who rob people of money and lives at sea, and do a living by licking blood from the knife edge. We have the impression that they are generally one-eyed dragons, and they cover their blindness with a black cloth. They also have the habit of burying treasures in the ground, and always draw a treasure map to make it easier for future generations to dig up.

However, few people know that pirate organizations are groups with a set of internal rules. The pirates were all unruly men with an independent spirit.

Let's start with an article in Scientific American, "The Logic of Murderous Pirates."

It is said that 5 robbers robbed 100 gold coins, and the way everyone decided to divide the spoils was: first the most ferocious pirate proposed a distribution plan, and then everyone voted on one person, and if 50% or more of the pirates agreed to this plan, then they would be distributed according to this plan; If less than 50% of the pirates agree, then the pirate who proposed the plan will be thrown out into the sea to feed the fish, and then the most vicious of the remaining pirates will come up with the plan, and so on.

Let's assume that these pirates are extremely clever and don't cooperate with each other, and that each pirate wants to get as much gold as possible. So, how will the first proposed pirate propose to get the proposal through and maximize the amount of gold?

To solve the "pirate split" problem, we always push forward from the last situation, so that we know what is a good and a bad strategy in the last step. Then apply the results of the last step to get the strategy that should be chosen in the penultimate step, and so on. If we start with the first step, it's easy to get stuck in a mental impasse because of the question: "If I made this decision, what would the next pirate do?" ”

Along these lines, first of all, we consider that only the last pirate remains, apparently he will give himself 100 gold coins and approve of himself. Going back to the decision that only Pirate Four and Pirate Five were left, Pirate Four could give him 100 coins and approve of him; Pirate Five was given 0 gold coins, and it was useless even if he objected. Back to Pirate Three, he can give Pirate Five 1 gold coin to get Pirate Five's consent; Gave himself 99 gold coins, and he agreed; Distribute four O gold coins to the pirates, and the four pirates oppose uselessness. Next, go back to Pirate 2, if you give Pirate 4 1 gold coin to get Pirate Four's consent; Gave himself 99 gold coins, and he agreed; Give Pirate Three and Pirate 50 gold coins, they will oppose but it is useless. Finally, we go back to Pirate One, where he can give Pirate Three and Pirate Five 1 gold coin each, and get the consent of Pirate Three and Pirate V; Gave himself 98 gold coins, and he agreed; Pirate 2 and Pirate 4 were given 0 gold each, and their objections didn't work.

Thus, the final result of the pirate split was that Pirate 1 offered to give himself 98 gold coins, Pirate 2 and Pirate 4 0 gold coins each, and Pirate 3 and Pirate 5 1 gold each. The proposal was passed, as Pirate One, Pirate Three, and Pirate Five agreed. Pirate 1 received the most gold under this premise.

In the previous stories, we were dealing with static games, which means that both sides of the game act at the same time. In reality, games are often dynamic and sequential, which requires us to consider how people will react to our actions in the future. "Pirate Split" is a typical dynamic game.

Let's look at another example of reverse induction – the ultimatum game.

It is said that passerby A found 100 yuan on the way, and this happened to be seen by passerby B. The two of them had a share, so they had to decide how to divide the money. We take the extreme assumption that their negotiation can only go on for one round, that is, passerby A proposes how much money to give to passerby B, and then passerby B says whether to accept or not to accept, if he accepts, he will share according to the proposal, and if not, then everyone has to hand over the 100 yuan to the police station, and no one can get it.

So how is passerby A divided? You might as well think for yourself first. In fact, this ultimatum game is a simplification of "pirate split", which is equivalent to two pirates splitting the money.

However, in real life, experts in game theory and experimental economics have done a lot of experiments around ultimatum games. This experiment was first carried out in Germany, and later in the United States, Europe, Israel, Japan, Southeast Asia, Russia and other countries and regions, and the results were roughly as follows: those who proposed a fairer distribution plan (40%-50% to the other party) accounted for 40%-60% of the subjects, of which half was the majority; 20%-30% of people put forward very unfair distribution plans (less than 30% to the other party), but these unfair proposals are always rejected by the other party with a high probability.

This may illustrate that people's real-world decisions are not based solely on economic motives, but often on the purpose of the other person's actions. For those who treat us well, we are often willing to sacrifice our own interests to give back, and for those who treat us badly, we are often willing to sacrifice our own interests to retaliate. Under such motives, less equal distribution is rejected as normal.

At present, there are actually two sides of modern game theory**, and this theory of explaining the observed real game behavior based on psychology and behavior is called "descriptive game theory"; And we blind people are extremely intelligent, rational, and concerned about economic interests to deduce the extremely complex consequences of human behavior, this set of games is called "standard game theory".