Well in the previous lecture, we have seen that any social problem can be formulated as a mathematical model of game. And now the question is the following. Can we find any single governing principle, which can be applied to solve all those social problems? Well, look at the examples we have seen, political campaigns, negotiation, market competition, traffic, and so on. All those social problems have common features. A, individuals try to do their best against others. B, under a certain set of rules. So since those, all those social problems share those two features, there is a hope to find a governing principle, a single principle, which can be applied to those social problems. Okay? So the question is the following, can we find anything like Newton's law of motion which can be applied to everything? In social science, in social problems. Okay, so let's focus on the first feature of all those, social problems. If the first feature says that individuals in a social problem try to do their, to do their best against others. Okay, so let's try to formulate this, aspect of social interaction by means of mathematics. Okay, so the basic idea is fairly, fairly simple. Suppose you have two alternatives, square alternative and a triangular alternative. And square is better for you. And this the, the other alternative, a triangular alternative, is worse. Okay? So you have a better choice and worse choice, and what would you do? Well, obviously, you choose the better one. Okay? So, this is not as perfect or accurate of Newton's law. Maybe sometimes you make mistake or sometimes you think that well, today I'm going to choose one of thing that's going to be fun. So this principle is not as perfect or accurate as Newton's law. But it does capture a very important driving force of human behavior. Okay? So let's try to come up with a single unified principle, which can be applied to all those social problems by means of this basic idea. Okay? So this basic idea is sometimes called the Assumption of Rationality. So rationality says that if you have better alternative and worse alternative, you choose the better one and I'll give you a very simple one. And you can assign pay-offs to those alternatives. You can assign a larger number two, for better one and smaller number, one, for example, for worse one and you maximize your payoff. So, rational choice can be formulated as maximizing your profit. So, your rational behavior can be formulated as maximization behavior, and you can apply mathematics to describe your behavior that's the basic idea. The next question is, is how far can we go with this basic idea? Okay, can we solve social problems only by means of this basic idea of rational choice. Okay? So to examine that question, let's compare two gambles, roulette and poker. 'Kay, so Mr. A is playing a roulette game or Mr B, Mr A is playing a poker game against, Miss B. So let's try to apply ration choice approach to those gambles. Okay, so, roulette and poker seem very similar they are gambles. But roulette is man versus a machine. But poker is man versus, versus man. Okay? And poker is the subject of game theory. And I'm going to argue that poker is substantially more complex than roulette, and let me explain why? Okay? So what is a rational behavior of Mr. A in roulette? Well, it's very easy to formulate as a mathematical model, because behavior of roulette machine is fixed. Okay? Each outcome happens with a positive probability, positive and equal probability so behavior is given. And given this probability to behavior of roulette, Mr. A can maximize his payoff. Okay? So maybe he has $100 and his task is to maximize his money, by betting on roulette 10 times, what would be the optimal strategy? Well, I don't know the answer, but you can certainly formulate this as a mathematical maximization or optimization problem, and use mathematics to determine Mr. A's behavior. So if the opponent's behavior is fixed, as in roulette game. Mr. A's behavior can be described by a very simple mathematical problem, of maximization of profit. Okay, so let's consider poker game. Okay, the difference here is that Mr. A is playing poker with Miss B, but Miss B's behavior is not given. So, therefore, it's not so clear what Mr. A should do in this situation. Okay, so what would you do if you don't know the behavior o, of your environment? What are you going to do if you don't know the weather tomorrow? Well, you form some expectation maybe it rains or maybe it's going to be fine. And those two events may happen with certain probabilities. Okay? So you form some expectation when your environment is uncertain. Okay? This guy here doesn't know exactly what Miss B is going to do, so he forms expectation. Okay? So the first task of Mr A is to predict Miss B's behaviour. Once prediction is given, Mr A can maximise his payoff. Okay? So, once prediction is given, then Mr A's behaviour can be formulated as mathematical optimisation or maximization problem. Okay? Is this the end of the story? Well I would argue no. Let me explain why. Okay? Miss B is not like roulette, the behavior of roulette is mechanically given. But, unlike roulette, Miss B is not choosing her behavior mechanically. Okay? She is another intelligent human being, so she must be thinking in the same way as Mr A is thinking. Okay, so to better predict B's behaviour, Mr A needs to examine what she is thinking about. That, that is what is called the strategic thinking. Okay, so a deeper strategic thought is as follows. Miss B is not like a roulette, she is another intelligent agent and he is, she is trying to predict what A is going to do. Okay? So to better predict Miss P's behave, B's behavior, Mr A tried to think that what she is thinking about It's own strategy. Okay? So a deeper strategic thought requires Mr. A's belief about Miss B's belief about Mr. A's behavior. Okay? So this is a deeper strategic thought, but think, but the ,uh, but the analysis doesn't stop here, you can go further and further. Okay? So to better predict with miss B's behavior, you have to think about A's belief about B's belief about A's belief about B's belief about A's behavior and so. Okay? This is the problem of infinite regress. Okay? If intelligent agents are trying to predict each other's behaviour and maximise their payoff, we end up with the infinite regress problem. So let me just summarise in strategic situation, in social problems, rationality alone fails to pin down individuals' behaviour the infinite regress problem. Therefore, we need a new mathematical theory. Okay? The simple mathematical model or mathematical theory of maximization is not enough, we need a new mathematical theory. And this is the basic reason why we need game theory. This basic difficulty was pointed out by the fathers of game theory Von Neumann and Oskar Morgenstern. Okay, so given this observation, finding a governing prin, principle, finding a single governing principle which can be applied to all those social problems, is a very challenging scientific problem.