So I have been giving you lots of reasons why people might play a Nash equilibrium, but now I have to address the issue that people might not play Nash equilibrium. I admit that people might not play Nash equilibrium, and I'm going to tell you if game theory is useful in those situations. Okay, so probably I gave you three reasons why people might play at Nash equilibrium. Probably the most important reason is dynamic adjustment, okay. People might not be so rational, they may not play at Nash equilibrium but by accumulating experience in the same game, or similar games, they eventually might play a Nash equilibrium, okay? So, if adjustment process ever converges to a certain point, the outcome ought to be a Nash equilibrium. Well, if the situation is not Nash equilibrium, there's at least one player who can deviate to increase his payoff, okay. So, the situation is not stable, and the adjustment process doesn't stop there, and goes on. So if the adjustment ever settles on a certain point, that should be Nash Equilibrium, okay, that's fine, but there is no guarantee that, you know, this adjustment process always converges, okay, so in that case, you know, the behavior might be chaotic, and even if adjustment process eventually does converge to a Nash equilibrium, it may take a very long time. So, if there is no guarantee at Nash, that the Nash equilibrium always emerges, is the concept of Nash equilibrium really useful? Okay, and so we start to meet, that people might not play a Nash equilibrium so let me address this issue, okay. My answer is yes, Nash equilibrium is still a very in, in, interesting and important and useful concept, and my answer is based on what is called a stylized fact. Okay, what is stylized fact? A stylized fact is a stable mode of behavior that is repeatedly observed. Okay, so let me give you an example people's behavior, or convention, on Tokyo subway escalators, 'kay. So this is the picture of Tokyo subway escalator, and if you are not in a hurry, you stand on the left side, and if you are in a hurry, you can walk or run on the right side, 'kay? This convention was formed around 1992. So, according to a leading, the newspaper, Asahi newspaper there was an article in February 24, 1992 saying that a new convention is being formed in Tokyo subway stations. On the escalators if standing you stay to the left so that anyone in a hurry can walk or run on the right side, and the article says this seems to be a spontaneous order formed by the busy commuters in Tokyo's subway stations. Okay, so this is what I call, this is a perfect example of what I call a stylized fact. This behavior is repeatedly observed day-by-day after 1992, and I would argue that this is a Nash equilibrium. If all other people are following this convention, it's best for you to follow the same convention. So if, if you are standing on the right-hand side, right side, you would be harassed by customers in a hurry, okay, so this is a Nash equilibrium. If you deviate, you will lose. Okay, so, in general, stylized facts are likely to be Nash equilibria, why? 'Kay, so if people are not following a Nash equilibrium by the very definition there's always some one who can gain by deviating. Right, Nash equilibrium said that nobody can gain by deviating. So in situations that are not Nash, someone can gain by deviating, okay? So sooner or later, such a profitable deviation is eventually discovered and people's behavior change, so the model behavior collapses. So it, it is no longer a stylized fact. So, therefore, if you find a stable mode of behavior, well which is repeatedly observed in a society, a stylized fact that is highly likely to be a Nash equilibrium, and the very important goal of any social science is to explain stylized fact and the stylized facts are likely to be Nash equilibria, okay. So this is probably one of the most important reasons why Nash equilibrium is useful in social sciences.