brief introduction

Cockfighting, as the name implies, is a confrontation between two cocks, and neither of them will obey the other, so they began to choke. You bite me, I kick you. However, if everyone is killed, the result is both sides lose. This horn was pecked blind and the chicken leg was pinched off. Then, even if the cockfighting is decided, it is meaningless. Therefore, the chicken game has two equilibrium points. These two equilibrium points are named after the mathematician Nash-Nash equilibrium point. The position of the equilibrium point is that one side wins, advances, and the other side retreats and makes some concessions. The point is no longer centered, but the golden section. Because neither side is willing to choose.

Therefore, both sides hope to gain the most benefits with the least loss. Therefore, the best result is that one side is tough and wins, while the other side compromises and loses. At this time, both sides will consciously abide by Nash equilibrium, which is also the best strategy of chicken game.

algorithm

Imagine two cocks meeting together. Each cock has two options for action: one is to retreat, and the other is to attack. If one party retreats, the other party doesn't, and the other party wins, the rooster will lose face; If the other side also retires, the two sides will be tied; If you don't retreat, the other party will retreat, you win and the other party loses; If both cocks advance, then both sides lose. Therefore, for every rooster, the best result is that the other party retires, not himself. The payment matrix is as follows:

Chicken B/ chicken a move back and forth.

Forward (-2, -2) (1,-1)

Returns (-1, 1) (- 1, 1)

The figures in the above table mean: if both people choose "forward", the result is that both people lose and both people get a -2 payment; If one party "advances" and the other party "retreats", the advancing rooster gets 1, winning face, and the retreating rooster gets-1, losing face, but not as much as both. Both of them "retired", both of them lost face and got the reward of-1 Of course, the figures in the table are only relative values.

There are two Nash equilibria in this game: one is forward and the other is backward. But the key is who goes in and who goes out. A game is predictable if there is a unique Nash equilibrium point, that is, this Nash equilibrium point is the only known game result in advance. But if a game has two or more Nash equilibrium points, no one can predict a result. So we can't predict the outcome of the chicken game, that is, we can't know who is going in and who is going out, who is losing and who is winning.

App application

The process of establishing the emperor in the Han army is a cockfighting process, not Liu He's cockfighting, but a game between the imperial clan children and the outlaw heroes in the Han army. Both sides hope to find a person who represents and defends their best interests, and let this person be emperor. According to the Records of the Later Han Dynasty, when establishing the emperor, many people thought that Liu was very suitable, but the outlaw wanted to establish:

(Greenwood Hero) Indulge in pleasure, fearing that "you will become bigger if you are rich, and you will become a saint and coward if you are greedy." . ("Were" Volume 14 "Liu Chuan")

phenomenon

Chicken-eating games are also common in life. In college, teamwork is often needed. Those students who don't care about the exam results and say "larger foe" can easily get a lift, because those who value their studies and grades have no reason to do their homework well in the team.

Such examples abound in society, and people who are often unreasonable and crazy are more likely to discourage rational people after an argument.

Based on the above examples, Gao Chengyuan believes that the game of eating chicken emphasizes the concept of "opportunity cost" to a great extent. People who lose more opportunity costs tend to be more rational, more restrained and more swayed by considerations of gain and loss, while people who lose less opportunity costs tend to be more unscrupulous in their lives.

A simple example, a traffic accident happened on the expressway, and a rogue and a scholar theorized. Because of the difference in time and cost, the game of eating chicken is easy to produce, and the final result is often one: it is unreasonable for a scholar to meet a scholar.

The game of eating chicken emphasizes how to gain benefits through compromise in the game. Gao Chengyuan believes that if the two sides put themselves in their shoes, they can negotiate on the issue of compensation and finally reach an agreement to exchange compensation for concessions, and the problem will be solved. There are often compromises in the game, and it is easier for both sides to reach an agreement if they can put themselves in their shoes. Consider how much compensation you get before you are willing to retire, and understand each other with your own ideas. It is difficult to break the deadlock if we only consider the problem from our own standpoint and are unwilling to give in and give some compensation to each other.