159, best Nash equilibrium

"Hey! Shao Fei, I won! It's me kissing you! ”

Liu Ying shouted behind Shao Fei, but Shao Fei couldn't run towards the station. Liu Ying limped and kicked off the ground, but she still walked back to the medical team with a happy smile.

Shao Fei came to the command room, but Zhao Fei was still pondering the problems of rock, scissors, and paper.

"Still haven't figured it out yet?"

Shao Fei patted Zhao Fei, sat down on his chair, took the paper and began to calculate.

Zhao Fei stepped forward and complained: "Shao Fei, you can't play with me like this, I won't be able to sleep at night." You have to explain what Nash equilibrium is. ”

Shao Fei said with a smile: "I'll teach you after this battle." I'll give you another topic, go back and think slowly, don't bother me now, ok? ”

"Okay, you can say it."

Shao Fei thought for a while and said, "A beautiful woman took the initiative to come over and talk to you and asked to play a game with you. The beautiful woman proposed: 'Let's each show the side of the ocean, positive or negative. If we are all heads, then I will give you 3 yuan, if we are all tails, I will give you 1 yuan, and you can give me 2 yuan for the rest of the situation. You go back and think about it, the beautiful woman's proposal is a profit or a loss. ”

Zhao Fei thought for a while and replied, "I should have earned it, right?" ”

"After thinking about it, you're answering me."

After Shao Fei finished speaking, he scratched on the paper, used all the available information, and used mathematical formulas to calculate the optimal Nash equilibrium.

Zhao Fei saw that Shao Fei was so serious, ={s1,...,sn:u1,...,un} Those formulas were incomprehensible books for Zhao Fei.

Based on the calculated data, Shao Fei began to draw up a battle plan.

In the early morning of the next day, Shao Fei immediately convened an operational meeting to lay out a plan of action.

First, Shao Fei wrote numbers in four directions on the map, East 3, South 8, West 2, North 7.

After finishing the painting, Shao Fei said: "This is the chance that the devil will attack the station. Based on this odds, I began to lay out the operational deployment. ”

Shao Fei ordered the commander of the second company: "The second company, responsible for the Japanese army attacking from Lexian in the south, there is a section of road here that is relatively rugged, and you have laid an ambush on the hillside. If the devil gains a foothold, evacuate immediately. The enemy chases and runs, the enemy stops and we go around, and the enemy retreats and I fight, and we must drag it out until night at the minimum cost. Remember the point of the order, not to eliminate but to delay. ”

The commander of the second company stood up and shouted, "Yes! ”

Shao Fei added: "Leave the second platoon commander Wei Liang and his 2 squads for me," he said. I'll give you a company of recruits, but you can't participate in the battle, it's to create a momentum and attract devils. I'm stressing, don't fall in love with the devil, keep a safe distance from the devil, and pay attention to your surroundings. ”

"Got it"

The second company commander didn't think about answering directly, and then returned to the chair. He felt that Shao Fei had always distrusted him.

"Company Commander."

"Here!"

Shao Fei ordered: "You take your first platoon, second platoon, and a company of recruits to the north." Thirty miles away from the station, an ambush was laid, and when the devil arrived, he only needed to drag it off, and the recruits would empty their guns in a hidden position to create momentum. The mission is not focused on elimination, but as much as possible to hide and wait for support. ”

"Yes!"

After Xu Pengfei sat down, Shao Fei said to Wei Liang: "Wei Liang, you take your two classes to the west." If there is a devil, just attack and slow down the devil's mobility. ”

"Yes|!"

Wei Liang finished shouting and sat back in his original position.

Shao Fei finally said: "The devil may be today, maybe tomorrow, we don't know." But in the morning they must go out, bring dry food for noon, and in the evening, if there are no devils, leave a squad on guard, and the rest of the people will go back to the station for dinner, and then return immediately. ”

After Shao Fei finished speaking, he sat down and said, "If there are any questions, bring them up now, and you will come out after breakfast after the meeting." ”

Zhao Fei asked, "You forgot to mention the road to the east of the station. ”

Shao Fei smiled: "There is a chance of 3 in the east, I gave up, after all, we are not strong enough."

Xu Pengfei asked with questions: "Why do the devils go far and near, and there is Sun Liancheng's brigade in the north." As far as I know, they have reached a thousand people in less than two months. Sun Liancheng also applied to the branch for the establishment of an independent regiment, but was rejected by the detachment leader. ”

After listening to this, Shao Fei said in an atmosphere: "Don't tell me about Sun Liancheng." That boy has a grudge against me. ”

Zhao Fei asked, "Don't you have an opinion, when did you make a feud?" ”

Shao Fei took a breath and said, "I'm going to sweep the detachment to report the situation, and I happened to meet that kid." If you fight a devil ambush, you will show off your might, show thousands of people, and want the formation of an independent regiment, can I do it? The establishment was higher than ours, so I suggested to the detachment commander in person and told him to go back to training. As a result, there was a feud. ”

"Hehehe" Zhao Fei laughed and pointed at Shao Fei: "Okay, let's get down to business, why don't devils come from the east?" ”

Shao Fei soothed his emotions and explained: "First, although the mountain road in the east is not very rugged, the mountains on both sides have high slopes, and ambushes can be fought everywhere, and we will be consumed to death before we reach the station. Second, Sun Liancheng's troops in the north were spreading too quickly. A thousand? The guns are not as many as my company, not to mention heavy weapons, and I am happy to get a few crooked handles, and there are a few of those company commanders and platoon commanders who have really led soldiers. Third, the devils of the two sides worked together to fight them, and Sun Liancheng was able to break through even if that kid had a big life, and he would still defend a P base. ”

Shao Fei's tone was still dissatisfied with Sun Liancheng, and then he sighed and said, "It's just that I pity the people in the base area." ”

Liu Ying asked, "What about our medical team?" ”

Shao Fei replied, "Stay at the station and wait for the arrangement." I'm just analyzing, the war is not 100 percent, and it's hard to figure out if the devils really advance from the east and west, and I left a main platoon and special combat team just in case of emergency. I will also arrange four fast horses to observe the battle in four directions. ”

Zhao Fei smiled and asked, "Everyone has arranged it, what about me, the captain?" ”

Shao Fei patted Zhao Fei and said with a smile: "You are our main general, of course you stay in the big tent and strategize." ”

Zhao Fei smiled ashamedly and said, "How do I feel that you are the captain." ”

Shao Fei replied: "At most, I am a dog-headed military division, and to put it bluntly, I am the chief of staff or something." The management planning of the troops, I am really inferior to you. ”

After listening to this, Zhao Fei still smiled, and then asked everyone, "Do you have any other questions?" ”

"No" "No" "......"

Zhao Fei got up and announced, "Break the meeting, go back and prepare well." ”

After everyone left, Shao Fei asked Zhao Fei: "Have you thought about that question yesterday, the beauty wins or you win." ”

Zhao Fei pointed at Shao Fei with great resentment: "You kid, I didn't sleep well all night, thinking about it, I always feel that I have a 2-to-1 chance, minus the odds of both sides, I should be able to win 8 points and 1 chance." ”

Shao Fei smiled and said, "It's a 1 in 8 chance, but it's just a beauty." ”

Shao Fei wrote the formula on paper: Suppose the probability of our heads is x, the probability of tails is 1-x, the probability of beauty heads is y, and the probability of tails is 1-y.

In order to maximize the benefits, we should have equal returns when the opponent goes heads or tails, so the equation is: 3x+*=*x+1*

Solve the equation to get x=3/8.

Similarly, the benefits of beauty, column equations

-3y+2=2y+*

The solution y is also equal to 3/8, and the expected income of the beauty each time is 2-3y = 1/8 yuan. This tells us that in the case that both parties adopt the optimal strategy, the average beauty wins 1/8 yuan each time.