Glamor Economics

Chapter 78

Is there a happy ending in Chapter 11, Section 5 - Nash Equilibrium
There is a well-known movie "A Beautiful Mind" about the protagonist Nash's unusual academic career. This movie has moved countless audiences to tears.Maybe people don't know that the protagonist's life prototype is Nash, the Nobel laureate in economics, who once proposed the famous "Nash Equilibrium" theory.This theory is a major development of game theory, and it can even be said to be a revolution.

Equilibrium is the final result of a game.Equilibrium is the combination of strategies composed of the best strategies selected by all players.Equilibrium means balance. In economics, equilibrium means that the relevant quantities are at a stable value.In the relationship between supply and demand, if a certain commodity market is at a certain price, everyone who wants to buy the commodity at this price can buy it, and everyone who wants to sell it can sell it, we say that the supply and demand of the commodity have reached equilibrium.The so-called Nash equilibrium is a stable game result.

There is such a story: Jack and Jim travel together.After a long walk, at noon, Jack and Jim were ready for lunch.Jack brought 3 pies and Jim brought 5 pies.They met a hungry passerby, and the passerby was hungry, Jack and Jim invited him to have dinner together, and the passerby accepted.Jack, Jim and passers-by ate all 8 cakes.After eating, passers-by thanked them for their lunch, gave them 8 gold coins, and continued on their way.

Jack and Jim started a dispute over the distribution of the 8 gold coins.Jim said: "I brought 5 pieces of cake, I should get 5 gold coins, and you should get 3 gold coins." Jack disagreed: "Since we eat these 8 pieces of cake together, we should divide the 8 gold coins equally." Jack insisted Thinking that each person has 4 gold coins, for this reason, Jack found the fair Shapri.

Shapri said: "Child, Jim gave you 3 gold coins, because you are friends, you should accept it. If you want justice, then I tell you, the fair division is that you deserve 1 gold coin, and you My friend Jim deserves 7 gold coins."

Jack didn't understand.Sharpley said, "Well, boy. The three of you ate 3 pies. You took 8 pies and Jim brought 3 pies. Eight pies in total. You ate 5/8 of them. That is 1/3 pieces, passers-by ate 8-3/3=8/3 of the pie you brought; your friend Jim also ate 1/3, passers-by ate 8-3/5 of the pie he brought =8/3. In this way, among the 7/3 pieces of cake eaten by passers-by, there are 8/3 of yours and 1/3 of Jim’s. According to this division, you can only get 7 gold coin.” According to Sharp After Li said this, Jack stopped clamoring for more points.Finally, Jack reached an agreement with Jim, and Jack only wanted 3 gold coins.

After the game between the two sides, the choice of the two sides is in line with the Nash equilibrium, because if Jack wants one more gold coin, Jim will be unbalanced, and if Jim wants one more gold coin, Jack will be unbalanced.Therefore, 1 gold coins for Jack and 1 gold coins for Jim are the best choices for both parties.

This optimal choice is the Nash equilibrium of the game between Jack and Jim.Because this choice leads to an outcome that will not be regretted, no matter what the other side does, both parties are satisfied with their strategy.In this Nash equilibrium, Jack is not necessarily satisfied with Jim's income, but Jack's strategy is the optimal strategy to deal with Jim's strategy (otherwise, he can only get [-] gold coin).

This is the Nash equilibrium, and now people use this theory to analyze various phenomena such as business competition and trade negotiations, and have made outstanding achievements.In economic life, Nash equilibrium is actually around us.

Every holiday is the time when there are the most people in the supermarket. If you are standing at the end of a long line next to the cashier with a pile of things in your arms, are you going to find the shortest line with the pile of things in your arms, or find the nearest one? queue?

Here we assume that everyone in the supermarket has a rational expectation - to leave the supermarket as soon as possible.So all the teams will be the same length, and you don't have to work hard to find the shortest team.As long as shoppers see that the next line is short, they will quickly join the shorter line, and the shorter line will grow longer until the two lines are evenly populated.This is the case for two adjacent teams. Similarly, all teams will have similar numbers.Therefore, it is best to choose the nearest one.

The result is the same if we consider it in terms of time.In addition to queuing up to see the length of each team, we also have to care about the speed of each team.If one team has 10 people, but everyone buys less, and the other team has 7 people, all pushing shopping carts and buying a bunch of things, obviously people still want to be in the first line.When the number of the first team exceeds that of the second team enough, the movement speed of the two teams is basically the same, and you don't need to find the team to line up.In addition, the proficiency of the cashier will also affect the speed of the team's movement. If you don't know which cashier is proficient, it is best to find a queue nearby.

It doesn't matter which team you line up in. This is what is called equilibrium in economics.Equilibrium is a state of balance of power, or a state of great satisfaction, which everyone is willing to accept; or a state of self-imposed entrapment, which everyone is forced to choose.But whether people like it or not, it's the best choice we can make.

[links to related words]

Dominant Strategies Every firm in a game usually has more than one competitive strategy, and the set of all of its strategies constitutes the firm's strategy set.In each enterprise's strategy set, if there is an optimal choice that has nothing to do with the strategies that other competitors may adopt, it is called the dominant strategy, and the other strategies relative to it are inferior strategies.

Dominant strategy is a technical term in game theory.The so-called dominant strategy refers to the competitive strategy that is the best choice of the enterprise no matter how the competitor responds.Obviously, in the process of the company's business competition, the party with the dominant strategy undoubtedly has a clear advantage and is in an active position in the competition.Dominant strategies are sometimes obvious.

(End of this chapter)