Separating equilibrium in Game Theory - Open Yale Course

Separating equilibrium is proposed by Michael Spence. This model told us the only thing that distinguishes the costs of good workers from bad workers in education is it is so painful to do the work. According to the class, separating equilibrium does not only concern the real money, but also adds the personal interest, talent, pain and suffering in cost difference.

I have some views different from Ben Polak’s. Let me introduce mine first. In my opinion, the income can be controlled, but the cost depends on some kinds like individual’s talent and very hard to change. In a normal and ideal society, the income of various occupations should not be too much, it means you almost get the same income, whatever you drive a dump truck or teach students in college. What exactly determines a person to become truck driver or professor is only the individual cost in different two things. In reality, the two incomes of teacher and driver are certainly not the same, but I think the different income is only determined by supply and demand. Here I don’t add this definition in.

Due to income – cost = profit

We can assume the two professions have the same income as 30.

Somebody A, who is very talented and interested in driving (the cost is 2), but not in teaching (the cost is 20), has two choices.

If he drives a dump truck, his profit is 30 – 2 =28

If he teaches the course like game theory in Yale University, his profit is only 30 – 20 =10.

In the class, he has to tolerate the naughty students, and prepare the class everyday. It is too horrible and so much pain and suffering for him. Apparently, 28 > 10, the comparative advantage for A is choosing driving dump truck.

Somebody B, who is very talented and interested in teaching (the cost is 5), but not in driving (the cost is 10), also has two choices.

If he drives a dump truck, his payoff is 30 – 10 =20

If he teaches the course like game theory in Yale University, his payoff is 30 – 5 =25.

Maybe he also has to tolerate the naughty students in the class, and prepare the class everyday, but the pain and suffering in the class is better than driving a dump truck. Apparently, 20 < 25, the comparative advantage for B is choosing teaching in class.

In this ideal society, each person would play their respective roles in their own areas of expertise. In other words, no matter what kind of occupation you do, you get paid well. Which profession you want to do is entirely determined by your talent and interest, and perhaps you will find driving a dump truck is happier than teaching in class.

What if there is too difference during the two income.

Also depends on Benefit – cost = profit.

But this time, the two professions have very quite different paid.

As a driver, he only can get 30.

As a professor, he can get 300.

Somebody A also has two choices. The cost of driving is still 2, because he has the same talent and interest in driving, the cost of teaching is still 20, because he also hates the naughty students very much. But this case is very different from above.

If he drives a dump truck, his profit is 30 – 2 =28

If he teaches the course, his profit is 300 – 20 =280

The result is though he hates teaching very much, but he has to tolerant all of this for the huge profit. Apparently, 28<<280, as a rational person A is going to choose teaching, even though he has lots of pain and suffering in class.

For somebody B also has two choices. The cost of driving is still 10, because he still don’t have much talent and interest in driving, the cost of teaching is still 5.

If he drives a dump truck, his profit is 30 – 10 =20

If he teaches the course, his profit is 300 – 5 =295

Apparently, 20<<295, as a rational person B is going to choose teaching.

Under this abnormal profit-driven, lots of people without teaching talent are going to join the teacher group, only in order to chase the good paid.

Here I agree Ben’s claim that some children have to be left behind, I don’t agree that education increases inequality, because teach students in accordance of their aptitude, it doesn’t mean unfair,. Dr. Ben was born in England, and got Dr. in U.S., so I can understand he cares about the weak side, but I have to note the purpose we establish the rules to distinguish the good from bad is not to distinguish them in their income, but help them to choose the best position. I think if Ben was born in China, he must know the harm of every person not in his position. When you can’t establish a good rule to achieve a separating equilibrium for everyone, people must take the advanced position with the only purpose that is maximize its own payoff. The person who didn’t have ability to be a judge is to be a judge, and the person who didn’t have ability to be a chairman is to be a chairman. The process when all children go to university is the process which is the dilution of elite education. The only result is qualification inflation, and you will see that in the country there are so many people who can get Dr. Degree, but lots of them suffer unemployment. In any period of human development, we all need one or two, like Nicolaus Copernicus or Isaac Newton who has unique point of difference, to lead the world people open a new page, but the public education must be going to make everyone average. Here I admit the disadvantages of elite education, which will make big gap between them, so I think the public education should be replaced by skills education.

Establishment of good rules is more important than whoever join the rules. This point reminds me the event of ConocoPhillips’ Bohai bay oil spill. Here I am not going to blame the United States company ConocoPhillips, because if I were the company, I also didn’t care about oil spill or not. Did any company dare to do that in U.S. or Canada? I don’t think so, the reason is very simple any company is going to be punished to pay huge cost by the law in U.S., but according to Chinese bullshit law, they only have pay 200 thousands Yuan at most. I remember some words by Thomas J. Dunning. “With adequate profit, capital is very bold. A certain 10 percent will ensure its employment anywhere; 20 percent certain will produce eagerness; 50 percent, positive audacity; 100 percent will make it ready to trample on all human laws; 300 percent., and there is not a crime at which it will scruple, nor a risk it will not run, even to the chance of its owner being hanged. ”

Each person or company prefers to maximize its own payoff, whatever from capitalism which is based on private ownership or socialism which under the name of public ownership, but is only for some privileged class self-interest. Every person or company is neutral, there is no good or bad person or company, but only good rules or bad rules.

   The problem of China food safety is very very serious. In previous years, maybe there are some companies didn’t do the bad things, but current, no company is not going to do bad things. Reasons are simple.

When a company A does the legitimate business, he can get income as 100, the cost is 80 and profit is 100-80=20.

When a company B does the illegal business, he also can get income as 100, but the cost is only 30, because he only uses the toxic and hazardous chemical materials, and his profit is 100-30=70.

Even if company A has a conscience and always does the safe food, the company B also can defeat the company A, just through the price war. Moreover, in a country without laws, you can’t rely on a moral or conscience to restrain a person or a company.

Prostitution and the Onion theory

Prostitution is a common problem we have met for a long time. From IMF Chief Kahn on rape charges in 2011, to Obama's bodyguards in prostitution scandal recently, we have to admit that prostitution never left our sight. Prostitution is legal in some countries, but illegal in other many countries. Here is a picture which can show you the details about prostitution in different countries. Apparently, red areas are much more than green and blue areas. As human beings, how do we rationally treat the problem of prostitution?

In order to treat this problem correctly, we must make thorough analysis to it. First, we have to figure out what the nature of the prostitution. In my opinion, the nature of prostitution is just a deal. We can take a look around those prostitutes, and most of them are living at the bottom without any skill for living, and they only depend on selling their vagina to survive, what is just natural resource given by God. According to the lesser of two evils principle, frankly speaking, choosing to rent the vagina is rational choice between itself and death. Of course, their choices also conform to Maslow's hierarchy of needs, and survival is most important. In nature, prostitutes are as same as those, who are blue-collar workers depending on skills for living, or who are professors depending on their mind and knowledge for living in famous universities, or who are great players depending on strong bodies and superb skills on basketball court or football field to get  10 millions dollars in pocket a year. The reason why they can get good pay is that the tangible or intangible assets they have can not be replaced, such as superb skills, wise minds or height, but the reason why prostitutes suffers so cheap is every female has a same cheap body asset – vagina. We can imagine that one day there is only one woman left, and how much is it if you want to have a sex with her. I think she will be priceless of the world. Prostitution is as same as other profession, just pays something out in order to get something back.

Why does prostitution suffer so serious criticisms? I think there are two main reasons:

1, due to people has not a very real understanding of sex, and we also link prostitution and sex together and think prostitution as immoral, evil and dirty.

2, in some male chauvinists or shameless scholars' eyes, prostitution is an unfair thing, because they claim that women can get double harvest both on physically and money, but men not only need to pay the money, but also have to work hard in vagina sweatily for women. This statement is very outrageous and absurd. I can give you an anti-example here: what if a man gets on an inflatable doll or a dead female body replaced a living woman, the man also will work hard on the top of them, and do you think male only work hard for the inflatable doll or dead body? The point that male work hard in vagina on bed just for women’s benefit is nonsense. Males are only for their own benefit to work so hard, of course the benefit is orgasm about 7 seconds shudder as return.

Every coin has two sides, costs and benefits. In fact, this theory just can be understood through mathematics in middle school. In my opinion, any sciences are connected, and start with one or two laws, and you can deduce everything just according to different areas.

We can define a formula like this:

B is the benefit what your want.

C is the cost what you have to pay in order to get the benefit B.

When C = 0, the formula of 

is meaningless or undefined.

Apparently, from mathematical point of view, we can deduce that the game only with benefit you want, but without any cost you should pay does not exist. Since division by zero is unbounded, it has no meaning, and so is not interpreted mathematically. So mathematicians say that, 'Division by zero is undefined.'

When P = 0, the formula of  

                            is always equal to zero.

It means that in any game, whatever you do or pay, you always can’t get your purpose from this game. You always get nothing, and then what should you do now? Mathematician will tell you only one way: make C also equal to zero, because in mathematics,  is called indeterminate form. Apparently, it

 tells us you can’t waste any cost in any game, if you can get nothing from it.

A classical example is “Not in my backyard”. In Taiwan, early NIMBY campaign under the slogan “chicken shit stayed in my backyard, the egg is in someone else”. Intelligent and rational people always don’t like to pay for the benefit of others.

The hierarchy of interests of every person is like an onion layers. The central interest is the core interest which person could give up anything to defend. Every rational person would give up the interests of the outer layer, in order to get the interests of the inner layer.

This onion theory is very similar to Maslow's hierarchy of needs, but there are still some differences between them.

1, Maslow’s theory is in two-dimensional, he just put the basic needs in the bottom, but onion theory is three-dimensional, I put it in the middle.

2, Maslow’s theory didn’t show the relationship between the two needs in the same level, but onion theory can show every need’s position in a person’s value.

3, Maslow’s needs are stable, not variable, and it can’t explain why somebody can sacrifice him/her self for a great aim, such as art, science or for special person, but onion theory thinks that every body has different hierarchy of interests in different situation, the hierarchy can be alterable under special case, and it also means the sequence can be changed by different case.

4, Maslow only told us people’ needs, but didn’t tell us the cost people would pay. Onion theory not only tells you the hierarchy of every one’s desire, but also the logical relationship between them.

On the issue of prostitution, the onion theory can explain it well.

According to the onion theory of prostitutes, living is in the center of every thing, more important than orgasm, and they can accept to rent her vagina to make living. So the deal is female get money to survive from male, but need to pay vagina out.

According to the onion theory of clients, having an orgasm on a woman is more close to the center than paying money. So the deal is male get a vagina to ejaculate from female, but need to pay money out.

I think money is the cheapest in people’s hierarchy of interests, because money is only used to satisfy the various needs of the people. I dare to say that if the client relies on the money to survive, he would never spend money on prostitutes, because he can masturbate to achieve orgasm.

About hard working in woman’s vagina is another deal, there is necessary and sufficient conditions between working hard and obtaining orgasm, in short, rubbing hard on his penis is sufficient condition of orgasm. I think one day women can figure out what is real female orgasm and how to get it, they also need hard working on her clitoral shaft to get the last shudder about 7 second.

Let's go back to the onion theory. I wrote that in my blog North Korea would never give up its nuclear test, regardless of whether U.S. gives food aid or not. In the eyes of that fat, his reign is the core interest of his onion, he didn’t care about nationals' survival or death at all. In other words, food aid from U.S. only benefits general public, but not him, the only one thing which can benefit him is nuclear threat. So if you want to have a deal with someone, you must have to know firstly what most important thing he cares. Wake up some ignorant people in the mind is rather more important than give them food. When whatever you pay, you always can’t get your purpose, there is only one rational decision you should make: make C also equal to 0. I think U.S. should take some more effective ways, not only just exercise in futility.

Finally, I just want to say, if you are a female, please don’t despise prostitutes, because you are a more unfortunate prostitute in some sense, but without pay. Maybe you are not lucky enough to be a female dung beetle, who only watch the males agonize over rolling the ball over to the hole while the female rides relaxed, just prepare to plant her eggs inside it (according to the Global Problems of Population Growth from Yale open course).

A famous Japanese AV girl called Aoi Sola once said that “The only purpose I am lying naked in front of a camera is just for living, but someone standing in front of a camera with well dressed is only for his lust and desire.”

The role of Hormone in Sex determination and differentiation

Sex hormone is another thorny issue in my theory system. Here firstly I want to claim that intersexuality, transgender, homosexuality and shemale are totally different conception in nature.

Intersexuality is identified as ambiguous genitals, commonly has a large clitoris or small penis. The reason is that crossing-over partial occurrence between X and Y chromosomes during father’s meiosis period then lead his offspring to be an intersex. Intersex is controlled by natural gene from parents, not by any sex hormones.

Transgender is identified who doesn’t identity his/her born gender, and do the surgery to artificially change the appearance, but not the genes. It obviously includes the psychological aspects, not only in the physiology. Not considering surgery (modern medicine), transgender is only identified as non-self-identity in psychology, and his/her body is as normal as male/female. I think psychological problem is also controlled by the natural gene.

Homosexuality is identified as who only loves the same gender as him/her self. It can be divided into two situations:

1, self-identity, it means he/she identifies him/her self as the born gender.

2, non-self-identity, it means he/she doesn’t identifies him/her self as the born gender, he/she wants to be the other gender.

Shemale is different from the three above. Famous shemales are always from Thailand, and most of them were from poor families and injected external estrogen when childhood. Ten years later, the male physical characteristics will gradually shrink, such as the male penis will become short and small, and the skin becomes nourish, the breast uplift. They look like as same as a normal female, but the genes they have is also XY.

Today I want to talk about the role of sex hormone which really suffered injustice. Human have two sex characteristics, one is called primary sexual characteristic, and the other is secondary sex characteristic.

1, Shape and structure of male and female genitals is called the primary sexual characteristic, decided by genetic material - chromosomes. It has been basically complete at the birth.

2, only the secondary sex characteristic is the result of sex hormones’ function in human.

There are almost no morphological differences between boys and girls before their puberty, although boys and girls still have testis and ovary. When entering puberty, the difference between men and women begin to appear with the increase of sex hormone levels. Estrogens are produced primarily by developing follicles in the ovaries, the corpus luteum, and the placenta. Follicle-stimulating hormone (FSH) stimulates the production of estrogen in the granulosa cells of the ovaries. Male levels of testosterone directly induce growth of the testicles and penis and indirectly (via dihydrotestosterone (DHT) the prostate. Estradiol and other hormones cause breasts to develop in females.

We can use logic way to reconsider that we can control the gender, if we think hormone is the key to intersex. If you want a boy, you can inject androgen from the beginning of your pregnant, and if you want a girl, you can inject estrogen. Do you think so? Absolutely not, it is so absurd. Hormone can do nothing in primary sexual characteristic. Primary sexual characteristic abnormal is only caused by genes. This is a causal question: Who decides who? Genes decide intersex or normal organs, then organs decide sex hormones secretion normal or abnormal.

I can give you another classic example here. There are some eunuchs in Chinese ancient palace whose penis and testis have been removed since he was little boy. I think the sex hormone in eunuch’s body have been in balance, neither androgen nor estrogen can prevail over each other. Notice here, these eunuchs are different from shemales, eunuchs don’t have testis, it means they can’t produce androgen, but they are not injected the external estrogen, so they neither show the male secondary sex characteristic, nor the female secondary sex characteristic. They look like enlarged version of little boy. The shemale is in different way. They still have penis and testis on his body, but they are injected estrogen since little boy, when entering puberty, they don’t show male secondary sex characteristic, but female secondary sex characteristic. Why do this happen? I think injection estrogen has destroyed the male normal sexual path, and secondary sex characteristic can’t be shown out under so much external estrogen, but they show some female secondary sex characteristic, such as breast uplift, slim waist and wide hips so forth and so on. They still have penis, testis, and scrotum, and penis can’t become into clitoris shaft, and scrotum still in fusion together can’t get into separated two piece labia majora, and the middle line is still in scrotum.

People always identify shemale as female, yes, they do look as same as female, but they are not real female and still have XY chromosomes. I made two pictures to illustrate the relationship between hormone and genes.

The above picture is the curve of human with XY chromosomes under different sex hormone. We can consider the black solid line as male physical normal development, and the red dotted line as shemale development. Androgen and estrogen almost get balance in blue dotted box, it also means the children whatever boys or girls before adolescence are under neutral appearance in the blue box, and you can’t even distinguish them by their face. When the androgen dominates, the boys get into masculinization, when the estrogen dominates, the boys get into shemale. Here I use anti-masculinization instead of feminization as same idea as particle and anti-particle, because I think if we use prefix “fe-” in the front of a word, it means she must be a she with XX, not XY. Masculinization and anti-masculinization here mean that the natures of them are same, just with different manifestations, as same as particle and anti-particle in physics.

Contrarily, the above picture is the curve of human with XX chromosomes under different sex hormone as the same idea as previous picture. We can consider the black solid line as female physical normal development, and the red dotted line as hefemale development. When the estrogen dominates, the girls get into feminization, when the androgen dominates, the girls get into hefemale. Here I use anti-feminization instead of masculinization, because I think if we use prefix “male-” in the front of a word, it means he must be a he with XY, not XX. Feminization and anti-feminization here mean that the natures of them are same, just with different manifestations.

Is there a really big sex gap between male and female?

Men are From Mars, Women are From Venus. Most of common relationship problems people think between two genders are that they come from distinct planets. The way males fall in love is with their eyes, and the way females fall in love is with their ears. Male maybe can't understand in his whole life why so many women are full of vanity and comparing with other women. Women also feel inconceivable why men are so addicted to sex and beautiful young women. I am very serious to say that it is because they live in different frequencies and share the different values. The reason why women suffer vanity is that they are with empty soul, not only lose their selves, but also live in other people's evaluation, discussions and praise. The reason why men are addicted to sex so much is that they only care about their own like or dislike and do not care about other people's evaluation or discussion.

Frankly speaking, men are rational, and women are irrational. Male logic is more conform to the principles of game theory than female. Here I am not going to talk about the details why female are irrational, in short, women always can’t get the central idea of things including sex. Here I want to talk about there is a really big sex gap between male and female from the different genital pictures, when the God created human beings.

1, What can we get from external genitalia anatomy what we called deformity?

The above picture is a comparison of the normal and abnormal female genital. Apparently, so-called abnormal female genital looks like a little boy's genitals, with an enlarged clitoris, urethra and vagina fused into one tube, two labia fused together into scrotum with a raphe in the middle. Notice here, there is also a raphe there in normal man. It shows that two pieces of scrotum didn’t stick together at the beginning, but with the development of the fetus, two pieces get into fusion together. Female genital deformity, for some reasons so far unknown, just develop into the other side of gender in fertilized egg development process. It is easy to see that clitoris and penis are homologous, labia and scrotum are homologous.

The above picture is male genital feminization. We can obviously see that the penis with under developed didn’t grow out of the main body, and two pieces of scrotum didn’t get fusion successfully in fertilized egg development process for some reasons. This abnormal male genital looks very similar with normal female genital.

The above is the development of male and female external genitalia, it is clear that in the process of development, male and female genitals are both from the same organization and structure at the beginning. Only during the development, men and women have the different ways to develop. About why women and men suffer feminization and masculinization, many experts believe that the changes of virilization or feminization are due to androgen or estrogen. I have no idea, if so, I have a question: why the probability of abnormal genital is so low? Because the androgen or estrogen is a concept of quantitative, and every body has both, only in different proportion, how do you define the proportion? If hormone is the real reason to lead deformity, the incidence of deformity should not be so low.

I don’t know that, but I think there is another possibility, in the process of father's spermatogonia meiosis, some genital gene fragments of the XY chromosomes have allelic exchange partly, as the result is the gametes X or Y is not pure as normal and they get some gene fragments originally not belong to them. However, due to the male once ejaculate thousands of sperm, and the proportion of so-called abnormal sperm is very low compared with normal sperm, so it reduces very low probability of ambiguous genitalia. I think it would be a rational reason.

The left picture above is a normal female vulva anatomy, the right one is that I add something according to my situation (PS: I thought I am normal, but I just thought). I have a strong shaft up to the forefront of my pubis. Every time, I need to rub my shaft rhythmically to get my orgasm. What’s more important, I can feel a little ball obviously in my right labia majora, and the left one is smaller than the right one. The location of the ball is slightly higher than clitoris, but lower than the other side of my shaft. Not only a ball, I also can feel a stem up attached to the ball. It feels like the stem to an apple, I can say that the ball grow out of my body.

Do you think that is very interesting? Yes, I think so. Let me try another perspective.

2, What can we get from internal genitalia anatomy

,

As it is known to all, males can’t ejaculate and urinate at the same time. Current theory claimed that male body has a system that keeps it from being able to ejaculate and urinate at the same time. During sexual arousal, muscles at the base of the bladder contract in order to close off the passageway from the bladder into the urethra, the tube through which urine and semen leave the body. This makes it impossible for urine to be released during ejaculation. So, men can feel free to relax and go with the flow, because they don’t pee when they come. For women, things are more complicated, it is easy to confuse the sensation of impending orgasm with the urge to pee. This is more common that women suffer urinary stress incontinence when approaching orgasm. Simply, women are really confused by the wrong feeling. In fact, female also can’t ejaculate and urinate at the same time, because women also have a valve to keep it from being able to ejaculate and urinate at the same time. You will feel incredible, but it is a fact. Moreover, this valve not only can prevent women peeing during sex, but also can prevent women peeing right after the orgasm immediately, and women would obviously feel they need to wait for a few seconds to open somewhere hard to release the urine. A lot of people claim that urinary incontinence is female ejaculation. I think this theory is absurd and stupid. This is all because people can’t figure out what a real female orgasm yet.

My inspiration from Pap test

The Pap test, also called a Pap smear, checks for changes in the cells of your cervix . The cervix is the lower part of the uterus (womb) that opens into the vagina (birth canal). The Pap test can tell if you have an infection, abnormal (unhealthy) cervical cells, or cervical cancer.

The following two pictures are normal cells examined under a microscope in Pap test. I got very surprised, when I first saw these pictures from internet, because I found these pictures from cervix are very similar to my pictures.

After every time I orgasm, I can always feel there will be a little mucus to flow out from my vagina. I collected it from vagina opening and put it under a microscope. The following pictures are my mucus after my ejaculation under microscope.

The following pictures are stained by Trypan Blue

1, Obviously, I can see that the number of cells from vagina opening after my ejaculation is far more than they get from cervix in Pap test.

2, My cells can be stained by Trypan Blue, it means these cells are dead (PS: I orgasm and get the sample in evening first day, and I put the sample under microscope in morning second day, about 12 hours time lag.)

My curiosity:

1, Why I can ejaculate so many dead cells?

Because of the Pap test sampled from cervix at the bottom of the uterus, I have enough reason to deduce that my dead cells are from uterus inside through Os. It also means uterus will discharge some mucus including lots of dead cells from cervix, while female orgasm.

2, Where are these cells from?

As you known, menstrual discharge is composed from the inside of the uterus, but apparently far different from the ejaculation mucus. Female menstruation period is approximately every 28 days, but every orgasm in every time I can ejaculate some mucus like this. If I orgasm several times a night, I can definitely feel that the quantity of mucus are progressively reduced, if in seventh time, I nearly ejaculate nothing out. I do think ejaculation is a very complicated process as same as menstruation.

3, Does the mucus contain gametes? Unfertilized egg or polarbodys.

In male ejaculation, male discharge sperm form testis out of body, why can’t female discharge something from ovarian out of body in real female orgasm. Everything is possible. Current theory claims that the unfertilized egg either dissolves or is absorbed into the body, but I don’t know it. I don’t think uterus have absorption function, if that way, uterus can absorb all menstrual blood, not to discharge them. I guess uterus only have excretory function through Os, including menstrual blood, baby and ejaculation mucus.

There are too many mysteries waiting for me to unlock, I really need God’s help, I believe God is an American.

Lesson 3 from Game Theory - Open Yale Course

Tipping point of Thomas Schelling

In this model, teacher told us point B (1, 0.5) is a strict equilibrium, and point C (0.5, 1) is weak equilibrium. Equilibrium B is a stable one, and it is difficult for people to move from equilibrium B to C. Equilibrium C is not stable one, and we are going to go back at equilibrium B, if we move away from C a little bit. There is a tipping point here. If you go beyond it, you will go to the other equilibrium. This point was called tipping point, proposed by Thomas Schelling.

I agree with Schelling very much, but teacher didn’t mention which the tipping point in this model. I have some personal thoughts about tipping point here and please let me explain for you.

If we want to move from equilibrium B to C, and it means there must have some people who can abandon their immediate benefits 0.5 to 0 right now, I think it is really hard for people, because people always only focus their own immediate benefits. Conversely, we have been equilibrium C (0.5, 1), a little bit people maybe 1 or two person move away, the payoffs of minority go down to the point K^/, and the majority’s payoffs go down to the point P^/. Although the payoffs of both are not equal, I don’t think the move can cause collapse of the system, because whether a system collapse or not depends on the choice the minority make. When they go down to the point K^/, they suffer a loss, but they still get payoffs more than 0.5 (equilibrium B). At this moment, the minority knows they can’t get more payoffs through their own efforts, and they will lose more and make everyone to 0.5, if all minority people move away, they have no choice, only depend on majority’s intelligence and rationality. Now the minority still has faith to this system, until the minority go down to the point K and get payoffs equal to 0.5 (equilibrium B). I think point K is the minority’s deadline, because if they go down to the point K^//, they suffer a loss than 0.5 (equilibrium B). At this moment, they don’t have to depend on others to increase their payoffs, but only on their own. They will betray immediately when a little bit down to the point K, and then system collapse just happens suddenly, because they don’t still have faith to this system. So I think the point K is tipping point in Thomas Schelling’s theory.

In the investigation of reality, a lot of tipping points are less than 50%. I think it because there is not linear function in reality. We should change our model for a little bit.

Let me change the linear to convex, it is more difficult to make equilibrium B to C, because of the low slope during AK, if someone wants to move equilibrium B to C, he will face more difficulty to get the point K. Conversely, it is easier to make equilibrium C to B, and only 20% of the minority betray to the other side, the system will collapse down. The system existence is only between X (0.4, 0.6), and the amplitude is 0.1. Well, what circumstance belongs to this function? Some system is with serious polarization between the rich and the poor, and under and middle classes are difficult to get rich through their efforts. The vast majority of people in the middle-lower class and a few people control the vast majority of the wealth. The rich get richer and the poor get poorer. The more polarization, the less X, and the system more easily collapse. This social system is not stable.

What if I change the linear to concave function? It is just the opposite to the convex function. The vast majority of people are in the middle-upper class, and the bottom of the people can easily reach the middle through their own efforts. The vast majority of people control the vast majority of the wealth. At least about 80% of the people betray to the other side, the system will collapse down. The system existence is between X (0.1, 0.9), and the amplitude is 0.4. This social system is the most stable and difficult to be subverted.

There is another thing we should consider, except the slope of the curve. What if we change the payoffs of betrayers? If we increase the payoffs from point B to B^/, the tipping point K immediately move from point K to K^/. System existence X is between (0.375, 0.625), and the amplitude will reduce to 0.125. If we decrease the payoffs from point B to B^//, the tipping point K immediately move from point K to K^//. System existence X is between (0.125, 0.875), and the amplitude will amplify to 0.375. So apparently the payoffs the betrayers get directly affect the system’s stability. 

I think research tipping point is very useful, particularly in the study of system stability. I also think everyone has their own tipping point in everything, there is no absolute loyalty, and everyone could betray you, when you cross his tipping point. Conversely, if you really want to overturn a system, you should pay attention to two things:

1, make the system more polarization.

2, pay as much to betrayers as you can.

Tipping point applies not only to a system, but also to the maintenance of the relationship between two people or two countries. “A nation has no permanent enemies and no permanent friends, only permanent interests." Winston Churchill said. Whether a man chooses betray or not totally depends on the position of tipping point. The theory of tipping point can apply to every area in our daily life.

By the way, because of the two points above, if I were Mr. President, I will do the opposite to the political asylum of Wang.

 

Battle of the sexes from zero-sum to win-win

                                       sex game

According to my theory of orgasm, I am sure male and female never can get two orgasms together. Here I make a table to show the payoffs of two people in sex game (it also applies to same sex.). If player 1 chooses to be active and player 2 chooses to be passive during a sex game, it means player 1 controls the rhythm and power, and how and where he stimulates arbitrarily by his instinct, until he gets his own purpose – orgasm, it means 1 is his payoffs. Frankly speaking as a passive one, player 2 doesn’t get 0 as her payoffs, but -1, because she can’t only get an orgasm as her payoffs, but the sex game costs her time and body as a tool for the other and vice versa. If play 1 and play 2 both choose to be passive in sex, the result is they can’t get orgasm neither, but don’t have to pay any costs, so it is (0, 0). If both are active to each other, it is a little complicated that each one wants to control rhythm and power by their own instinct, and the result is there will be an irreconcilable conflict between them, and neither can get the own purpose, but pay the costs. So it is (-1,-1). Apparently, (-1,-1) is a strictly dominated strategy for both of them.

It looks like a strictly competitive game as zero-sum between male and female. Precisely, that’s it during orgasm mode, but what we should pay attention to is whether we can make sex game from zero-sum to win-win. In today's world, the concept of zero-sum is gradually replaced by concept of win-win, but I think the zero-sum game will never disappear. Win-win is just a cooperative game, and it needs a lot of things as preconditions.

First, you want to negotiate. Well, the problem is when you need a negotiation with the others. Only in one case: when your payoffs directly or indirectly will be affected by other people’s decision, you should ask for a negotiation. This effect can be positive or negative, but the result of your offer may be not successful. For example, in the Prisoner's Dilemma game, confession is a strictly dominate strategy for each side, but finally they both have suffered a heavier sentence, because there is no opportunity for them to have a collusion before.

When your payoffs will not be affected by anyone under any condition, you can control this game all by yourself, and no need to ask for any negotiation. When there is a conflict between your interests and other’s, theoretically you can totally ignore any interests of other people, just do whatever you want to do. There is no need to have any negotiation for you here. For example, if you are alone, you can decide whether and where you have a lunch by your own mind, and no need to care about other people eat or not.

After you ask for a negotiation to someone, it may not be able to achieve a win-win situation. It depends on the following items.

1, both sides must be intelligent and rational decision-makers. They both have a clear understanding to strengths and weaknesses of two sides, and know what the core interests and the deadline of each side. In one word, they share the same common knowledge. Of course, if the other side is psychopath, you do not need to make any effort to get win-win situation, because he can’t play cards by common sense.

2, both sides want to have a benefit exchange. The important thing is the benefit each want to exchange is not their own core interests, and of course what each gets at least more important than each pays. When the core interests contradiction between the two sides, it is impossible to achieve win-win strategy, and then the game between them just becomes a zero-sum game. For example, two gladiators on the battlefield, only a person can survive, life is their core interests, and there is nothing more important than their own life. The negotiation between them can’t be successful, because of the contradiction between their core interests. The game is you die or I die - zero-sum game. You can refute me that Jack sacrifices his life in order to save Rose in Titanic. I will tell you that because in the interest balance system of Jack, rose’s life is more central than his life. There is no denying that jack can’t give up his life for any other one on Titanic.

3, they should trust each other. When you are going to achieve win-win strategy with others, you must have to consider whether the other side you can trust or not. Win-win game is a game which is designed in a way that all participants can profit from it, but not at the same time. In many cases, the payoffs are sequential in a game, can’t happen simultaneously. Maybe you get your benefits right now from the resolution, but the other only can get his benefits after a while. I think you deserve to be trusted more important than trust others.

There are 3 necessary conditions to reach a win-win, like Prisoner's Dilemma, they are both rational people and both want to have a collusion, but they don’t trust each other, and of course they can’t reach a win-win situation. They only can choose to maximize their own payoffs.

In conclusion, not every zero-sum game can be converted into a win-win game. Here I apply these 3 points to sex game, let’s try to figure out how to analyze this game and find some possible resolutions.

1, they are intelligent and rational decision-makers. Males were, but females were not. So far women can’t figure out yet what intelligent and rational decision is for themselves in sex game, I think I can awaken women’s awareness sooner or later after I unlock the mystery of female orgasm to the public.

2, there are some benefits on each side they both want to exchange for. I think it is hard for every rational person, because orgasm is core interests for everyone as physiological needs, male or female both can’t give it up. Human nature is selfish, so this problem is really difficult to solve. Maybe you can do it by yourself, but I think it is not a permanent solution. Maybe you can pay to find a whore, but what if you want to orgasm with some one you love. There is only one way you two have to orgasm one by one.

3, trust each other in sex game. I think you two should trust each other, if you really love each other. Notice that the biggest obstacle between two people in love isn’t the trust problem, but a physiological response - refractory period. Frankly speaking, It is all by human nature and really hard to overcome.

Sorry I really don’t know what Nash equilibrium is.