Choice of attack direction (Game Theory tricks)

In the multi-party game, we have decided to launch an attack against one of our opponents, but we have not been able to take advantage of the strength. What should we do at this time? The following story will give us some inspiration.

 

During the period of the Republic of China, there was a triplicate trend in Guangxi: Huang shaotao and Li zongrenhe had more than 20 thousand people, Lu rongting had more than 30 thousand people, and Shen Hongying had more than 20 thousand people. One year, Lu rongting and Shen Hongying fought in Guilin for more than three months, regardless of the outcome. At this time, Li Zongren, who sat down in the mountains and watched tigers, suddenly heard Lu and Shen began to merge.

 

Li Zongren believes that if both parties agree to the same agreement, Guangxi is still a three-point game. Lu and Shen have to work together for him and never miss the opportunity. So he discussed the war with Bai Chongxi and Huang xuchu. Bai Chongxi and Li Zongren coincide. He said: "Lu and Shen are in a hurry. We have been in the fire for more than three months. Now the fire is going to go out. If we do not take the opportunity to kill, we will lose the opportunity." Huang xuchu said, "Commander-in-Chief Li, do you think that Lu and Shen are the two of us going to better fight the land first? Or should we sink it first ?"

 

Li Zongren believes: "In the moral sense, we should first discuss Shen, Because Shen is capricious and has long been hated by the people of Guangdong and Guangdong, and he is determined to be a great man. As for Lu rongting, there is no general sense of guilt in Guangxi ."

 

Bai Chongxi said: "I think there are three reasons to fight land first. First, Lu is located in Guilin and Nanning, and is the political center in Guangxi. His defense is empty and easy to attack. Second, the land is connected to Hunan, and Hunan receives assistance from Wu peifu, which should not be supported yet. If you do not want to attack your website. Third, the attacker attacked Shen Hongying and won the game. The land forces are still there, and Guangxi still cannot be unified. If it is defeated, it cannot beat Lu or Wu. We are in the same situation as Han Xin in the fight between the Chu and Han Dynasties. When the united land is defeated, the united land is defeated, and the united land is defeated. We should conduct a strong weak attack to avoid real attacks ."

 

Huang xuchu said: "I also think we should fight Lu rongting first. Land, Shen battle, Lu rongting will be the main force to Guilin reinforcements, the rear of Nanning must be empty, therefore, our army attacked Nanning will succeed. In addition, Lu rongting was surrounded for three months in Guilin, and his life was exhausted. Even if we can defeat Shen Jun, there will be huge casualties ."

 

After full negotiation, the three men finally made a "land first and then Shen" decision and decided to attack Lu rongting first. Li Zongren led the launch of power-on, and asked Lu rongting to go down. After power-on, the Coalition forces split the land and water into different regions in Nanning. A month later, the left-wing army commanded by Li Zongren took over Nanning. The right-wing army directed by Bai Chongxi swept back to the left after the enemies of Binyang, Qian Jiang, and shanglin

Wu Ming was immediately attacked, and there was no fierce resistance. The two armies joined Nanning. Lu rongting, surrounded by Guilin, lost the base of Nanning and had to enter Hunan. Later, Li Zongren cut down Shen Hongying and tan haoming in less than three years to unify Guangxi in the autumn of 1925.

 

This well-known campaign with many victories has given countless inspirations to researchers of different generations. But in fact, apart from the favorable environment and other factors at that time, Li Zongren and Bai Chongxi are also full of the wisdom of Game Theory for the direction and order of attacks.

 

The Game Theory Course at Princeton University in the United States has such an exercise.

 

During a military drill, the Red Army used the troops of two divisions to conquer a city occupied by the Blue Army, while the Blue Army defended the troops of three divisions, the Red Square and the blue square each division have identical equipment, personnel, and logistics, and have the same natural combat capability.

 

Because the combat power is the same, when the two armies met, the majority of the teams won, and the war was "easy to defend against". Therefore, when the number of the two sides was equal, the defender won. At the same time, the smallest unit of the army is the division, and it cannot be further divided, as long as the red side can break through the line of defense, even if the red side wins: on the contrary, the blue side wins,

 

Assume that the Red Square has two directions for attacking the blue square: A and B. The blue square also has two directions for defending. In this way, there are three strategies for the solution:

(1) The two divisions attack the direction of the blue line of defense:

(2) The Division is divided into two ways. One division is attacking the direction of the blue line defense, and the other is attacking the B direction of the blue line defense.

(3) The two divisions attack in the B direction of the blue line defense,

 

The defender's blue square has four different defensive strategies:

(1) The three Division focuses on the direction.

(2) Two divisions guard direction A and one division defends direction B.

(3) one division defends against a and the other Division defends against B.

(4) The three Division focuses on defending B.

 

We will list the results of different policy combinations by means of permutation and combination. See table 7-1.

Red/blue Strategy 1 2 3 4

1. Blue wins. Blue wins. Red wins. Red wins.

2. Red wins: Blue wins: Red wins

3. Red wins: Blue wins

Table 7-1 game matrix between red and blue sides

 

In this game, the red party has no disadvantage strategy, while the blue party has a disadvantage strategy. Obviously, the blue side chooses the first strategy, that is, to assign three divisions to defend the direction inferior to the second strategy, that is, to assign two divisions to guard the direction and the other to defend the B direction. Because, the result of selecting the second policy by the blue side is no worse than that of selecting the first policy.

 

In Table 7-1, we can see three results: when the red party chooses the first strategy, the blue Party selects the second one, which is the same as the first one, and the red party chooses the second one, the blue party chooses the second strategy to win, while the first strategy is to fail. Naturally, it is better to choose the second strategy. When the red party chooses the third strategy, the blue Party selects the first and second strategies with the same results, all failed. It can be seen that the blue side chooses the second strategy, which is naturally better than the first one. Similarly, the third strategy is better than the fourth one. That is to say, both the First and Fourth strategies are inferior strategies.

 

From the perspective of rational people, the disadvantage strategy is a strategy that the blue party will not adopt. The red party knows that the blue party will not choose the first and fourth strategies. Therefore, both the red and blue sides know that the game can be simplified as shown in Table 7-2.

Red/blue Strategy 2 3

1. The blue square wins the Red Square wins

2. Blue wins

3. Red Square wins and blue square wins

Table 7-2 Simplified red-blue game Matrix

 

In this simplified game, the blue party has no disadvantage strategy, but the red party has a disadvantage strategy, that is, the second strategy, which chooses to divide the two-way attacking defense lines. Obviously, the outcome of the red Party's second strategy is that it is impossible to win, and the rational red party will naturally not choose this disadvantage strategy. The game matrix is further simplified, as shown in table 7-3.

Red/blue Strategy 2 3

1. The blue square wins the Red Square wins

3. Red Square wins and blue square wins

Table 7-3 The simplified red-blue game Matrix

 

At this time, the red and blue sides share the same situation, that is, although the red side is inferior to the blue side in terms of the total strength, but in fact, as long as it uses strategy to attack it, its chances of winning is the same as that of the blue side.

 

In game theory, the principle of "winning by the weak" is true. Just as in the Battle of chengpu, the Chu-state coalition forces with dominant troops cannot guarantee their advantages in some regions (such as the right army), while the general troops are in a weak Jin army, however, it is possible to skillfully concentrate on the excellent strength of the army, win the first battle in the right direction of the Chu army, then defeat the left army, and defeat the two wings to defeat the Chu army,

 

The same is true in enterprise competition. Enterprises that are at a disadvantage in capital, scale, brand, and manpower can concentrate and integrate all their resources in a certain market, as a result, it leads to a strong enterprise advantage in the market segment and becomes the winner in the market competition.