Game Theory #1: The Dating Game

This semester we are going to analyze a question together, which is how do societies behave? Why do we do what we do? What motivates us? What drives us? And there have been different theories as to what drives human behavior. So let's go over some theories. The first theory comes to us from religion. And the idea is that we are all driven in a war between good and evil. There's a good side to us, and there is an evil side to us. There's Satan and there's God, and we are constantly in a battle in ourselves. Okay? Do we move towards Satan or do we move towards God? And that's the core of human civilization. So religion is meant to give us the strength to show us the path towards goodness. That's one theory. Another theory comes to us from biology, and the idea is sex. We want to pass on our genes forward because that's the point of our existence. If we cannot have children, we all will die. So the point of our existence is to have children and have them pass on their genes to others. Okay? And for males and females, life is different because as a man, you have a penis, and all you have to do is stick your penis into a woman and you're good, okay? That's all you have to do. So you want to stick your penis into as many women as possible, and that's the point of your existence. But as a woman, your life is different because it's hard to give birth. It takes nine months to incubate the child in your womb. And then childbirth is the most painful experience anyone will ever experience. And then the child, It'll take like 16, 18 years to raise a child to maturity. So it's a huge investment on your part. So as a female, you have to be very cautious, very careful about who you marry or who you have sex with. Okay? And so life is a struggle between men who want to put their penis into anything and women who want to be careful about who they marry. Okay? So that's the idea of biology. Then, of course, you have the idea of race and culture. That the world is a struggle between these different races and cultures for dominance. And each race, each culture has their own characteristics. Okay? So maybe the yellow race, they're very clever, but they're very weak. And then the white race are brave, but kind of stupid. The black people, like. Anyway, anyway, that's another theory. I'm not saying it's correct. I'm just saying it's a theory that people believe in. Then you have economics, right? And what they believe is that we are driven by money or self interest. We want to make as much money as possible, and that's what drives us, okay, that's pretty simple. And the last big theory is the idea of liberalism that comes from the Enlightenment. And here the theory is that history is a progress towards enlightenment, to rationality, to truth and to justice. So the inevitability of history, of human development is towards paradise, towards heaven. And maybe, you know, we go off track now and then, but inevitably we move towards God. And this comes to us from the Enlightenment. We call this liberalism. Okay, so these are five theories. There are others, but these are five theories that show you the diversity, the variety of ideas out there. What I will do this semester is present to you another theory which I call game theory. And my argument to you is that game theory is the best way to understand how humans behave. What drives nations, what drives societies, what drives humans. Okay? So that's my argument to you this semester. So the entire semester we will study game theory. All right? So what is game theory? All right? Game theory is very simple. The idea is that there are three components to a game, just three aspects to a game. There are the players, the participants, okay? Then there are the rules or the constraints. In mathematics, we would call this the boundary conditions, okay? The limits to the game. And the third aspect are the incentives. Basically, how do you win this game? What do you get from this game? My argument to you this semester is that if you study all three, okay? If you figure out who the players are, if you understand the rules, you understand the incentives, then you understand how the game works. And then, therefore, you can predict how the game will turn out, okay? That's the skill that I want to teach you this semester. And what I want to show you, or what I promise you, is that if you learn game theory, there'll be three major benefits to you as a student. Again, you don't have to learn game theory. You don't even have to come to class. But if you spend the effort to learn game theory from me, then three things will benefit you, okay? The first benefit is that you become a better person. The point of education, guys, it's not to get good grades or get any university or get a good job. What I believe is the point of education is to make you into a better person, which means that you are a much more thoughtful person who can better analyze yourself and the world around you. This allows you to make better decisions. This makes you a much more curious, much more moral and much more imaginative person, okay? So one benefit of learning Game theory is you become smarter and therefore you become a better person. Okay? That's number one. Number two is you'll be able to understand the world that we live in, because this world is kind of stupid. Okay? So you may have heard that Donald Trump and the American military went into Venezuela for no real, for no good reason, kidnapped a president of Venezuela, which is against international law, and then brought him back to New York City where he will stand trial. It's really stupid what happened. But then. But our class, it's not meant to say this is stupid or this is wrong because we all know it's stupid and wrong. We're trying to figure out why this happened and what this will lead to. We will be in this class studying and analyzing current events to understand how the world really works, why people behave the way they do, and understand how the game of the world works. And this requires you to actually follow the news. It's not hard to spend five minutes and just read up on the news. But we'll be looking at the war in Ukraine, we'll be looking at a new war between Israel and Iran. We'll be looking at what's happening in South America. We'll be looking at the conflict between China and Japan. We'll be looking at the relationship between the United States and China. Okay? So this is relevant to your lives because you will eventually have to work and live in this really screwed up world that we live in. Okay? And the third benefit is once you understand the game, you will have predictive powers. You'll be able to understand how the world will develop. You'll be able to analyze your own life and understand how you will develop. And that gives you control, sovereignty over your own destiny, okay? That's my promise to you. If you actually spend the time to listen carefully in class, to participate fully, to follow the news, and you spend the entire semester doing so, then these three benefits will start to accrue in you, okay? This is a lifelong struggle to learn game theory. I'm a lot older than you are, I have a lot more experience than you, okay? But I want to show you how to look at the world through game theory. Another phrase that you learn in school is, I'm going to teach you how to think critically about the world, or I'll just teach you how to think. Okay? All right? Are we clear? Any questions before I move on? Alright, so this is all very abstract. And so what I'm going to do now is I'm going to use an example of a game to show you how game theory works. Okay? All right, so let's use a really simple game. Let's imagine there are five boys and five girls and they want to get married. Okay? So these are the players. And what we're going to do is we're going to divide them up into male and female. Then what we're going to do is we will rank the males and the females. So we're going to rank 10 players into 5, 4, 3, 2, 1. 5, 4, 4, 3, 2, one. Okay, and so how do we rank them? Well, we rank them according to their attractiveness using three criteria. The first is genes, the second is wealth, and the third is status. Okay, so genes is very simple. It means that you are good looking, it means you're tall, it means you're healthy, you will live a long time. Okay? Genes is pretty simple to understand. Wealth just means that you and your family have a lot of money. Status means that you have a lot of friends, you have a high status job, you come from a really powerful family. Okay? So these are the three criteria that we can use to judge a person's attractiveness. And then what we can do is rank them from five to one. Five means really the best one means the worst. Okay? And we can rank all 10 according to these metrics. So according to biology, what we call evolutionary biology or evolution psychology, we're always trying to find the best genes to procreate because this ensures that our genes pass on. Okay? So remember that men have a penis which they can stick into anything. Women have to give birth. So their strategies are different. Okay, so basically five, number five is trying to have sex with all five women, right? That's his strategy. But female number five wants to ensure that she only gets five. Okay, so these are different strategies. And if this. According to evolutionary psychology, all five of these females should try to procreate with number five. Okay, but we know you can't do this. It's suicidal. Why is it suicidal? Because the human rights could survive. Right? It'd be idiotic to do something like this where all five women are just trying to marry this one guy and maybe him. Okay? But these three are eliminated because then your society would collapse. You can have that many children, so this can possibly be true. Right? So let's figure out what rationally, what should happen. Okay? All right, so let's think about this rationally or from an economics perspective. All right, so again, number five, he's trying to maximize the game. So he's trying to sleep with all five women. Okay? The problem, if he does that is these five know they're all being played, and they recognize that this guy is probably an asshole. So five, the best woman is like, you know what? There's not much of a difference between 4 and 5, so I'll just go marry this guy, right? So number four is gone. Number four is like, you know what? Five is probably making a good decision, so I'll just go marry number three, right? And then what happens now is that five, by trying to marry all the women, is stuck with the worst choice, right? So that's kind of stupid for him. He's stuck with number one. But guess what? If any of these guys try this crap, the same thing happens to him where four is like, you know what? I can't get five, but I'll try to get four and three together. And then three is like, screw you, I'm going to go and marry two. Four is going to marry three, okay? Then he's stuck with one as well, or he's just alone. So if they try to individually maximize their outcome, they all get screwed in the end. So the only way out of this is that they cooperate, okay? And the best way to cooperate is basically five is like, you know what? Screw this. I'm not gonna go after four or three. I'll just have my five, okay? Right? Four is like, yeah, I'll just go marry four. No dating, no games. I'll just go marry four. And three marries three, two marries two, and one marries one, okay? And the world now is perfect. Everyone has a husband and a wife, and they can now just have children. The world is perfect. And this is actually the best strategy for all the players, right? We call this the wording game theory we use for this is called the Nash equilibrium. Nash equilibrium just means that you always reach a state in which all the players maximize their outcome, the Nash equilibrium. And so the world makes sense. Now, there's a problem with this, though. The problem is in real life, no one does this, okay? In real life, no one actually follows this rule. Natural is just a theory we made up. But in real life, that's just not what happens. What happens in real life is we choose to be suicidal, okay? So let me tell you about a game I played. So last year, I was teaching this class, and I asked the boys, and I asked the girls, pretend you are now 30 years old, right? Your parents are pestering you to get married, and you've been on the dating market for 10 years. There's really no one that you think is perfect for you. You have basically Given up on love. Imagine that you want to get married now. And tell me, what is the minimum requirement you need in order to agree to marry someone else? Okay, what's the minimum? Okay, and then I have the boys and the girls write down response. The boys were pretty simple, right? Well, you know, as long as she likes me, and as long as I can put my penis into her, I'm good. Okay. It's that simple. Okay. It really is. Guys are like, yeah, I'll settle for anything. That's the boys, right? Girls were different. Girls were like, okay, if I don't love him, if I'm not even attracted to him, I need about a million dollars a month. Yeah, I need about a million dollars last semester. Okay. All right, so this makes no sense, right? So in theory. In theory, we should follow the Nash equilibrium. But in real life, what happens is this. All the girls want this one guy, okay? And maybe number four, they'll settle for number four. But three, two, one, they don't want. We know, because just look at the world around you. Look at these billionaires like Elon Musk. How many wives does he have? How many children does he have? All the women in the world, Many, not all, but many just want to marry actors like Brad Pitt. Billionaires like Elon Musk, right? And three, two and one. They. What do they do? Well, they watch Netflix, they watch porn, they play video games. They've given up on life, okay? They're like, we don't care. We call these people incels, right? Involuntary celibates, because they basically, they given up on life and life has given up on them. So this entire competition is between number five and four for all the woman in the world. And this is, again, suicidal. This will lead to the death of humanity. And the question now is, okay, why are we suicidal? And so let's look at game theory, analysis, right? The players, the rules, and incentives. We know what the players are. The players are doing stupid things. The rules we know. But incentives is something that we have to think about. Why are they behaving like this? And the answer is because they're not interested in sex or procreation. What they're interested in is status, okay? That's the game they're playing, status. I don't want to marry someone to have children. I want to marry someone so I can take a picture of her and post it on Instagram so I can get a lot of likes. I want to marry someone so I can walk over in the mall and all the guys are jealous. I want to Marry someone who I can brag about, okay? It's a game about status, not a game about sex or procreation. You understand? People are not being rational here. People are trying to maximize their status in life and that's why everyone's behaving like this. She may be the ugliest woman in the world, but she's still like, you know what? It's still my choice whether to have kids. And having kids is a pain in the ass. So if I'm going to make the sacrifice, this guy better be good looking, okay? Or this guy better be rich. Otherwise why would I want to have kids? Okay? So this is why people behave the way they do. If you think about this way, what you recognize is that people are rational but don't understand why they're rational. You, you have to figure out what the game is. Okay? But then this leads to a short question which is, okay, well, clearly this is wrong, because if we behave like this throughout human history, we wouldn't be here today. Okay? How is it that we have this game today and we're going to die, but we must have come from somewhere. We've been around for like a long time. So, so how is it that humans have survived for so long doing these stupid things? And the answer is basic game changes over time according to the superstructure of society. Okay, the superstructure. The superstructure is what determines the nature of the game. Superstructure is just think about the big picture, right? How many people are there? Is a society wealthy or poor? Are there enemies to this society? Okay, this is the superstructure, the big picture. Demographics, economics, culture, politics, religion. And these things together is what determines the nature of the game. So let's look at three examples of superstructure. All right? Example one is you have a low population society, okay? Low population is like maybe 200 people. 200 people, okay? A village. Basically, they are poor and low technology. Low techologies means they don't have access to clean water. They don't know what hygiene is. They don't understand what germs are. So it's very easy for a woman to die in childbirth, okay? And low competition. Low competition just means that there are no competing villages against them. Okay, so that's one kind of superstructure. The earliest superstructure of human society, okay? Then you have maybe growing population, okay? So we're talking like maybe 10,000 people, 20,000 people. They are now growing in wealth, growing wealth. They have some technology, meaning they have access to clean water and they have high competition, okay? Meaning that they're competing against different villages and societies around them, okay? That's enough superstructure. The third superstructure is overpopulation, okay? Which is the world we live in today, okay? Where in China you have a billion people. That's a lot of people. Too much wealth. Okay? But with wealth you have inequality, right? And then you have high technology. This high technology just means that every woman who gives birth will not die. And every child born will live off. Will live, okay? And then you have something called equilibrium. Equilibrium just means that, yeah, there's competition, but they're not going to go to war against each other. The world is basically peaceful, okay? And according to superstructure, the game is going to change. So let's go back to the game. Okay? We have 10 people in a low population, poor society. Guess what? They're not going to date. What they're going to do is they might get married, but they're going to have sex with each other. Why? Because as a woman, the only way to ensure that your child survives is if all the men in the village want to protect and nurture the child. And they will do that if they believe that the child could be theirs. Okay? So the woman will maybe have a husband, but the woman will also choose to sleep with other men to disguise paternity. Does it make sense? So there's no dating. There's just lots and lots of sex in order to maintain social cohesion. Okay? Now, in a superstructure number two, there's no dating either. Why? Because this society is in competition with other societies and they need to have as many children as possible. So what? The solution here is to have arrange marriages. Arrange marriages where, you know, who cares who you marry? Just have lots and lots of kids, okay? There's no dating either. Just have lots and lots of kids. You marry who your parents tell you to marry. You marry someone that you know, you marry your childhood best friend, who cares? But you marry someone, you have lots and lots of kids. That's superstructure number two. Superstructure number three is the one we live in. And here you have a dating game, right? Why? Because the odds of you obtaining status is really, really low, okay? And the only way that you can change your status is, is by marrying up. And that's why you have a dating game. A dating game is opportunity for you to find someone better than your social demographic circumstance can suggest, okay? And that's why you have low, decreasing fertility rate, where over time, because of the dating game, society will collapse. Okay? Does that make sense? All right, so now you're the government. And around the world, women who are wealthy, well educated are refusing to have children, especially In East Asia right now, the fertility rate in China is about 1, okay? About 1. The replacement rate that you need is a 2.1. So just to maintain your current population levels, every woman in China needs to give birth to at least two kids. But right now, on average, women are children, have one kid only in China. And. And the worst thing is that this trend is increasing. So five years ago, the fertility rate was maybe 1.7. Now it's 1. Okay? So the trend is very, very negative, okay? So governments all around the world are trying to figure out what to do. How do you convince women to have more kids? And what we've discovered is it's impossible. We can pay you more money like they do in South Korea. Guess what? It doesn't work because people don't want money. They want status. And status is a zero sum game, okay? Money is infinite, but status power is a zero sum game. So when you have overpopulation, we have too many people competing for too few status positions. You have decreasing fertility rate, and there's nothing you can do about it. The moment you give woman choice, they choose to improve their lives by marrying someone better, okay? Not all, but most. And so over time, what happens is your society collapses. If you look at history, the best indicator that a society is about to collapse is if the women who are wealthy and well educated, if they refuse to have children, this is the same. This is what happened to the Romans who collapsed. This is what happened to many empires. This is what's happening around the world today in America, in Britain, in Europe and China, okay? And this tells us that society is collapsing. So in other words, what this really is, okay, these superstructures, it tells us the life cycle of a civilization, right? So this is when. When civilization is young, then it mature, it grows, and then it collapses, okay? And if you look at history, all civilizations go through this process of birth, maturation and then collapse. And there's no way around it. So the power of game theory is that just by studying one aspect, okay? If I just study this game, all right, I figure out who the players are, the rules and incentives, I can figure out what the superstructure of the civilization is, okay? And then once I have these two, I can now figure out where it came from and where it's going, okay? That's what I want to teach you in this class. How to analyze a situation so you understand the players, the rules and incentives, which will give you insight into a superstructure so that you can figure out where it came from. And then you can also predict where it's going, all right, so. But you can also look at the superstructure and figure out what the game is being played. So this is one example. But. But throughout the semester, we'll be doing many, many different examples of game theory. Is this clear so far? Are there any questions, any comments, any questions before I move on? All right, All right, so let's just look at some basic facts, okay? All right, this is a map of the world, okay? As you can see. Okay, sorry. So the color scheme is this. The red is where the population, the society has an above replacement fertility rate, okay? So above 2.1, if it's dark red, like here in the middle of Africa, it's 6 to 7 or 6 above, okay? And why isn't that the case? Because Africa, in a situation where it is a growing society with middling tech, so a lot of people die, lots of competition. So to survive, families have to give birth to a lot of kids, okay? They have no choice in the matter. But then you move to the rest of the world, okay? So this is North America, Europe and East Asia, the three wealthiest parts of the world. And guess what? The fertility rate is collapsing because now we've entered the end game where it is overpopulation, too much wealth, so too much inequality. And so women are forced to pick the best possible mate or not have children at all. All right? And here the situation is very, very dire. North America and Europe are kind of. Okay, well why? Because of immigration. Because even though their women are not having children, they can choose to import people for their labor force. But East Asia is really, really screwed, guys. Okay, so just look at this region, okay? So China is one, but the worst is North Korea. Sorry, South Korea. South Korea has the lowest population rate in, sorry, the lowest fertility rate in the world. They're at between 0.6 to 0.8. So they're probably gone in 50 years time. It's so bad that when you go to South Korea, there are signs outside restaurants that says no dogs and no kids. They think that kids are a problem, okay? So you look at these areas again, they are poorer. So women are forced to have more children in order to survive, okay? But you look at wealthy areas, well, they're probably gone in 100 years time. It's total collapse. The solution that governments are choosing right now is to import immigrants, okay? Especially so these are the trends right now. And it's causing a lot of disruption in society because guess what, guys, People don't like outsiders. People don't like immigrants, but they don't have a Choice matter, because along with the fertility crisis, it's the aging crisis, where your population is getting older and older. Okay? So life, the world is not that simple. If you want to know who will rule the world in 100 years time, just figure out which society. In which society do wealthy, well educated women choose to have children, and then that society will rule the world. Okay, it's that simple, right? Well, unfortunately, if you do it that way, you get a really, really disturbing answer. Okay, so this is per capita gdp. Okay, so how much people make? All right, so obviously if you're zero, you're very poor. And if you move to over here, you're very wealthy. Okay, so United States is the wealthiest society in the world, right? Sure, we can understand that. Then this is the fertility rate, which tells us how many children women have on average. Okay? So again, 2.1 is replacement rate. Okay, 2.1 is replacement Rate. So the United States is actually below replacement rate. But the United States doesn't really care because it can import immigrants. Okay, China is probably around here somewhere. Okay. Angola is up here, but it's poor. So what this map tells us is a country that is most likely to be dominant for the next 50 years. Is. This country Israel. Okay? It is the only wealthy western high tech society in which women choose to have more than two kids. This is what game theory teaches us. And yeah, I know there are people like, yeah, but Israel, it's, it has 9 million people and it's in the middle of a desert and everyone hates Israel. I understand that, thank you very much. Okay, I understand that. But if you just analyze how the game works, okay, if you just look at it objectively from a game theory perspective, you are forced to conclude that Israel right now has the major advantage over everyone else. Now, it is possible that societies will change the fertility rate as the, as the world changes. Okay? But I'm saying that given the current state of all things Israel, their growth trajectory is very, very high. But then the question then is, okay, why is it that Israel, they are different from everyone else? And the answer is because the world hates them. Because they think they are different from everyone else and they must unite together to survive. So in Israel, fertility is status. Okay? If you are a woman and you give birth to a lot of kids, that means that you love Israel. That means that you are doing what you can in this war for survival. It means you are a patriot. Okay? But this has to do with religion. So what the west has done is not only has it created a dating game where women can choose to have kids. But the Western world has also given up on religion and embraced materialism, right? So what is valued in our world in the west, it's not patriotism or love of family or religious duty. It's just how many Instagram followers you have, it's how many YouTube subscribers you have, it's how many, how much money you have, okay? That's all that matters. So given the current state of state of events, it's very hard for the Western world and really for China to survive for the next 50 years, okay? And I know like, well, China has a billion people. So even though, you know, we're only giving birth to 10 million kids a year, which will still be around for a long, long time, okay? So at this rate, by 2100, China will be, will be at a population about 600 million. That's still a lot of people, man. Okay, here's the problem though. This is South Korea. South Korea is like the worst case scenario. And for South Korea, this is actually the best case scenario where, okay, given current trends and let's just pretend that nothing bad happens for South Korea. Well, by the year 2100, you have a situation like this where the vast majority of people are over 65 and you have no kids, okay? That is a zombie society where no one works and everyone just, I don't know, walks around the park every day. No one works. So the economy has collapsed, okay? So look at this trend where we are now in here, okay? With the majority, it's still a working population, which is good. You need that for the economy. But by the time you hit 2040, okay, you've got this huge dependency and a creating population. Okay? Do you guys see this where we are? So we're at 2020, right? Okay. All right, so it's still not too bad. But by the time you hit 2040, look at this, okay, look at this, look at this. Where you have absolutely no kids and then you have lots and lots of retirees, okay? And then by the time you hit 2060, oh my God, right? Your population, your working population has decreased by half, by 50%. All right? So if things are stay the same, if nothing happens, South Korea will be dead in, I don't know, by 2150, okay? Best case scenario. But what we know from history is that society should not die naturally. Eventually South Korea will be forced into wars, new economic crises. So this trend will just increase. And so if North Korea got past 2080, I'd be very surprised, okay? I'd be surprised by 2040 South Korea were to face collapse as a nation state because you need these people to work. But guess what? You also need them fight wars. So if North Korea ever threatens South Korea, most of your adult population will be dead. Okay? So South Korea cannot fight a war. Now, the prospects for South Korea is utterly hopeless. There's nothing South Korea can do about this because South Korea is an extremely materialistic society where the only way to get ahead is by making a lot of money. Okay? And if you're a middle class person in South Korea, it makes no sense for you to have three kids. It makes sense for you to have one kid and put all your resources into this one kid in the hopes that he passes the college examination, gets in a good university, and then gets a good job at Samsung, which is the only company in South Korea. Okay? Samsung, right. So the situation is pretty dire in South Korea. All right. Okay, that's it for today. Any questions guys, about what we've learned? Okay, Yeah, speaking of. Mic please. So for the last graph that we talked about Israel and I've noticed that the Saudi Arabia that is also like at half not bad GDP per capita and fertility risk. But for Saudi Arabia, maybe I'm wrong stereotypically that they didn't receive much hate as Israel. These. So we where did they at the similar position as Israel? That's actually a really good question. Okay, all right, so Saudi Arabia, as you can see from this map, has, it's a very wealthy society and families have about four kids on average. All right, so Saudi Arabia is actually an outlier. And, and the reason why is that it gets all its money from oil, oil revenues. Okay, so it sells with oil around the world. What does it do? It creates a welfare state using this oil. So you're incentivized to have many children as possible because the government will pay for it. Free schooling, free health care, free housing, and then a guaranteed job. So it's basically like socialism. It's also a Muslim country. So you have this religious duty imperative to have as many children as possible. Okay? But the problem, Saudi Arabia is the idea of human capital where it is not really a modern society in which people are well educated and they're contributing to the, to the economy. Okay? Saudi Arabia just gets all its money from oil and that's it. It's trying to grow terrorism, it's trying to develop its human capital, but it doesn't really work. Okay, so you're right in that Saudi Arabia, it seems to be doing well, but it's not really. Okay, but also People will argue about Israel as well. We're like, well, Israel gets all its money from the United States and it's the American military that supports Israel. That's true to a certain extent. But I would argue that if you actually go to Israel, you will see that it's an open, dynamic society in which you are allowed to ask questions, which you're allowed to criticize the government, in which you are given a lots of opportunities for social mobility. Okay? So Israel has democracy, it has innovation, okay? It has technology. Okay? And Saudi Arabia doesn't have these things. If you want to be a really strong nation, then you need innovation, you need openness, you need technology. Okay? It's also really highly educated, Right? Okay. Does that make sense? So Saudi Arabia, it's really an outlier here. But the problem is what happens if Saudi Arabia runs out of oil? Right. Or there's a war in the Middle east and Saudi Arabia is kind of screwed. But you can also argue, no. Well, you know, Saudi Arabia, it has a lot of money and maybe. Okay, so game theory doesn't give us the answers. Game theory, it just gives us a guide to ask questions and do research. Okay. Does that make sense? Yep. I have a question about, like, when is this data? It wrote about 2009. Right? So how about now? Did it change a lot? Or like, is there anything change? Okay. Okay. Yeah. So you asked about the sourcing of the data. Okay. And you're right in that there'll be fluctuation. Okay, but the. But this is 2024. Okay, 2024. And this is Israel right here. Okay. All right, so if it's red, it's a buff replacement. All right? And if you just Google Israel, population fertility rate. Israel is the only wealthy nation in the world that has an above replacement fertility rate. Okay. All right. Okay. Any more questions, guys? All right, great. So I will see you guys next class.