Ratchet to Cooperative Evolution
The tit-for-tat strategy works well in static groups, but what about in a dynamic group?
In order to answer this question, the experimenter uses the principle of ecology to analyze, assuming that the strategic group composed of players is evolved from generation to generation, and the rules of evolution include:
1. Trial and error. When people deal with their surroundings, they don't know what to do at first, so they try and do whatever works best
2. Genetics. If a person is cooperative, his offspring will have more cooperative genes
3. Learn. The process of the competition is the process of the opponents learning from each other. The strategy of tit-for-tat is good, and some people are willing to learn
According to this idea, it is assumed that among the 63 participants, whoever has the highest score in the first round, the proportion of the group in the second round will increase accordingly, so that the structure of the group will gradually change, it can be seen that the group is In what direction did it evolve.
The results are interesting
1. Tit for Tit The initial ratio was 1/63, and after 1000 generations, the structure stabilized and the ratio was 24%.
2. Some programs disappear during evolution
Experiments show
1. Groups are increasingly cooperative
2. The success of a strategy should be based on the success of the opponent. The tit-for-tat strategy cannot exceed the opponent's score in a 2-player game, at most a tie, but it has the highest total score, and the Harrington program is not. In this way, when it gets a high score, the other party must get a low score. Its success is based on the failure of others, and the loser is always eliminated. When the loser is eliminated, this program takes advantage of the loser. also eliminated
Limitations of the tit-for-tat strategy
Once a misunderstanding occurs, the 2-for-tat strategy will never cooperate, but instead choose to betray.
In reality, misunderstandings can easily occur, so the tit-for-tat strategy has 2 flaws in the real world
1. Too easy to inspire betrayal
2. Lack of a mechanism for declaring "This is it"
So, there are 2 ways to solve the dilemma
1. Generous tit-for-tat strategy: with a certain probability not to retaliate for the other’s betrayal
2. The tit-for-tat strategy of repentance: take the initiative to stop betrayal with a certain probability
Exrod states:
1. Friendship is not a necessary condition for cooperation. Even enemies may cooperate as long as the conditions for continued relationship and mutual return are met.
2. Cooperation does not depend on goodwill, good faith or the arbitration of an outsider, and may also arise from self-serving calculations.
For example, the principle of "live by yourself and let others live" developed during World War I. The German and British armies encountered a three-month rainy season in trench warfare. Guns kill people, as long as the other side does the same. The reason this principle works is that both armies are in a difficult situation and 3 months gives them a chance to adapt to each other
The Hostage Dilemma: The Prisoner's Dilemma of Multiple People
Adam Smith wrote in The Wealth of Nations that when individuals pursue self-interest, the invisible hand of the market will lead to the best economic consequences. increase.
This kind of rationality aiming at maximizing individual interests is called " individual rationality "
However, the Prisoner's Dilemma reveals the contradiction between the rational choice of individuals and the rational choice of groups, and behaviors based on individual interests often fail to achieve the best interests of the group . At the same time, it also reveals the inherent contradiction of market rationality itself. The behavior from individual rationality may not be able to truly realize the individual's best interests in the end, and even get quite poor results.
It can be proved that in the process of people's interaction, the egoistic decision-making results of each actor may be efficient or inefficient, but repeating such a decision many times is definitely inefficient.
Strategies in chaotic systems
Bar Game: There are 100 people who love to go to bars. Every weekend these people have to decide whether to go to a bar or stay at home. The capacity of the bar is limited, which means seating is limited. If a lot of people go, people going to the bar will feel uncomfortable. At this point, they are more comfortable staying at home than going to a bar. Suppose the capacity of the bar is 60 people, if someone predicts that the number of people going to the bar exceeds 60 people, his decision is not to go, and vice versa. How do these 100 people make the decision to go or not to go?
The result of the computer simulation is that a stable ecology will eventually be formed. The average number of people going to the bar will soon stabilize to 60 people, while the study of real people has found that the number of people going to the bar shows a regular wave shape.
Week i 44 people
Week i+1 76 people
Week i+2 23 people
Week i+3 77 people
Week i+4 45 people
Week i+5 66 people
Week i+6 78 people
......
Traditional economics believes that the actions of economic agents are based on deductive reasoning, but this is not the case. Most people's actions are based on induction. Therefore, in the bar game, people predict the number of people who go to the bar based on past history. The number of people, then the number of historical figures is very important, but the past history can be "arbitrary", so the future is uncertain. Issues such as stock buying and selling are extensions of the pub game model
Realistic inspiration of bar game:
1. From the perspective of a nonlinear system as a whole, its changes are unpredictable. To take correct decisions, it is necessary to understand its changing laws.
2. A nonlinear chaotic system is a system that cannot be fully understood, and we cannot know where quantitative changes will lead to qualitative changes
3. Individuals in chaotic systems can also adopt appropriate strategies in unpredictable processes. The minority strategy is the focus of our attention
The idea of straight lines and simplification has dominated our minds since Newton, yet this year scientists have discovered that the world is not so simple, it does not evolve in straight lines, but in association and interaction . In other words, the world is full of unpredictable chaos. The whole of a linear system equals the addition of its parts, so each part of the system is free to do its own thing without caring about the other parts. In nonlinear systems, the whole is not equal to the sum of all parts, it may be greater than the sum of all parts, because everything in the system is related.
Minority strategy
So is it possible to intervene in a chaotic system to reverse it in our desired direction? The answer is yes, and one of the ways is the minority strategy.
Example: A person found that the sanitary conditions in the village were very poor, and every street was dirty. He wanted to change the habits of the villagers, but it was difficult to convince them. He thought about it for a long time, and finally bought a beautiful dress for the villagers. a little girl. After the little girl put on the skirt, the girl's father found that her dirty hands were very incompatible with the beautiful skirt, so he gave her a good bath. But her father found that the messy environment in the house had soiled the skirt, so her father mobilized the family to clean the house well, and the whole house became clean. Soon the father came out of the clean house, and the aisle full of rubbish at the door made people uncomfortable, so he mobilized his family to clean the aisle at the door, or the neighbors found that the environment next door was too comfortable, and put the inside and outside of the house. After cleaning, the whole village changed.
Gunslinger Game
Three gunmen, A, B, and C, who hate each other, prepare for a duel. Spear A is the best, with eight out of ten; Spear B is the next best, with six out of ten; Spear C is the worst, with four out of ten.
First question: If three people fired at the same time, and each fired only one; after the first round of gunfights, who has a better chance of surviving?
Most people think that A's marksmanship is good, and the possibility of surviving is higher. But the logical conclusion is that C with the worst marksmanship has the best chance of surviving.
Let's analyze the strategies of each shooter.
Gunner A must shoot Gunner B first. Because B is a greater threat to A than C is to A, A should kill B first, which is A's best strategy. By the same token, Gunner B's best strategy is to aim the first shot at A. Once B kills A, and B and C compete, the probability of B winning is naturally much higher. Gunner C's best strategy is also to shoot A first. After all, B's marksmanship is worse than that of A. C kills A first and then fights against B. C's survival probability is still higher. Let's calculate the survival probability of the three gunmen in the above situation:
A: 24% (40% X 60% = 24% shot by B and C)
B: 20% (100% shot by A - 80% = 20%)
C: 100% (no one shoots C)
Through probability analysis, we found that C with the worst marksmanship has the highest chance of surviving, and the survival odds of A and B with better marksmanship are much lower than that of C.
Now change the way of play, three people take turns to shoot, who has a better chance? Still C
Join C to shoot first, what should he do? Empty the gun, as long as it doesn't break the current situation, he is always profitable
There are 2 forms of games: simultaneous game and successive move game
Conclusion: In the multi-party game, staying out of the game is also a consideration.
Duplicate elimination strategy
Example: In a military exercise, the red side will use 2 divisions to conquer a city occupied by the blue side. The blue side's defensive strength is 3 divisions
Condition 1: The division-level units of the Red Army and the Blue Army have the same combat effectiveness
Condition 2: The smallest unit of the army is a division
Condition 3: In the war, it is easy to defend and difficult to attack. When the troops are the same, the defending side wins
Condition 4: There are 2 directions to attack, namely A direction and B direction
Phase 1:
There are 3 offensive strategies for the red team
Strategy 1: 2 divisions attack direction A
Strategy 2: 2 divisions attack direction B
Strategy 3: 1 division in each direction A and B to attack
There are 4 defensive strategies for the blue side
Strategy 1: 3 divisions focus on defending direction A
Strategy 2: 2 divisions to defend direction A, 1 division to defend direction B
Strategy 3: 2 divisions defend B direction, 1 division defend A direction
Strategy 4: 3 divisions focus on defending direction B
After analysis, it can be seen that: the blue team has a disadvantaged strategy, and the blue team chooses strategy 1 worse than strategy 2, because strategy 1 cannot prevent the red team's strategy 3, and similarly the blue team's strategy 4 is worse than strategy 3.
According to the rational game principle: never choose a strictly inferior strategy , therefore, the blue-side strategy can be simplified, leaving only strategy 2 and strategy 3.
Stage 2:
After eliminating the blue-side disadvantaged strategy
Red's strategy:
Strategy 1: 2 divisions attack direction A
Strategy 2: 2 divisions attack direction B
Strategy 3: 1 division in each direction A and B to attack
Blue's strategy:
Strategy 1: 2 divisions to defend direction A, 1 division to defend direction B
Strategy 2: 2 divisions to defend B direction, 1 division to defend A direction
At this time, the blue team has no inferior strategy, but the red team has an inferior strategy, that is, strategy 3. At this time, choosing strategy 3 will definitely fail.
After eliminating the disadvantaged strategies of the red team again, there are only 2 strategies left for the red team and the blue team. At this time, the winning rate of each party is 50%.
Conclusion: The red team is inferior in military strength to the blue team, but the winning rate is 50%, which is the same in the enterprise competition. Enterprises that are at a disadvantage in capital, scale, brand and manpower can concentrate all their resources and integrate them in a certain local market, resulting in an advantage over the strong enterprises in the segmented market, thus becoming the winner in the market competition.