Okay, in the second lecture I'm going to tell you about what is called the coordination game and I'm going to talk also about intriguing phenomenon called self-fulfilling prophecy, okay, so let me start with a very simple example. A game played by two players- suppose two friends are going to collaborate on a computer job, so they are going to buy their own PCs, and PCs come with keyboards, Right? And there are several different designs for keyboards. Okay, so the choice of keyboard one choice is what is called the QWERTY, this is a design which everybody uses nowadays, so this is the design widely used, and there's another design called Dvorak, and it's designed for faster typing. So let me show you the pictures of QWERTY and Dvorak. So what we have here is QWERTY keyboard, that what- that's what we usually use. And, why is it called QWERTY? Well, the letters QWERTY are here. So that's why it's called the QWERTY keyboard, and on the other hand, Dvorak was designed for faster typing, and one important characteristic of Dvorak is all vowels are located here, okay. So why we have this QWERTY keyboard? It's a de facto standard. De facto standard of technology means that everybody uses this format of technology. So QWERTY is the de facto standard and it was a design originally adopted by the first generation of mass produced typewriter in the 19th century. Okay, and so, QWERTY was not explicitly designed for optimal typing, fastest possible typing. Okay, therefore the most efficient keyboard design is highly likely to be different from what we use today, okay? The most efficient design is likely to be different from QWERTY, okay? So, what about the Dvorak? Well, Dvorak was designed for a faster typing, but it may not be the optimal design. Okay, so let's consider choice between QWERTY and the optimal keyboard. Okay, so, the situation can be, again, summarized by a simple table, payoffs table. So, there are two players, two friends choosing keyboard design. Player one's choice is either to choose QWERTY or the optimal keyboard, and likewise player two has- has the choice between QWERTY and the optimal design, and if they both, if they choose different designs, then it's very inconvenient. So let's suppose their payoffs are low, say zero, if they choose different designs, and if they both choose QWERTY, they're happier and their payoffs are one, and if they both choose the optimal keyboard, they are even happier and their payoffs are two, okay. So, this is a very simple game and obviously there are two Nash equilibria: QWERTY equilibrium. I'm using QWERTY because my friend is using QWERTY, and my friend is using QWERTY because I'm using QWERTY. Okay, the other equilibrium is the optimal keyboard equilibrium and people are happier here. Okay, so important lesson you should learn from this very simple example, if that a game may have many Nash equilibria. Ma- Nash equilibrium is not usually unique. So the same society may have lots of equilibria. Okay, lesson number two, and moreover, one equilibrium say optimal equilibrium, can be better than the other, for all players, 'kay, so the same society may have good equilibrium for everybody, and bad equilibrium for everybody, okay. So the game we play about the choice of keyboard design is much more complicated because we have more players but this simple game indicates that our society may have lots of equilibria in y equilibrium is where everybody uses QWERTY. This is the equilibrium we play now but there could be another equilibria, another possible social situation in the same society where everybody uses the optimal design. Okay, so once the society is trapped in a bad equilibrium it's really difficult to get out, 'kay, by the very definition of Nash equilibrium, if you are the only person switching from QWERTY to the optimal design, it doesn't pay. Okay, so to move from bad equilibrium to good equilibrium, everybody should move simultaneously. It, it's a very difficult task. Okay, and the same simple game, coordination game tells you about interesting things about the choice of technology. Okay, when new technology is invented, it may come in several different formats, okay. So about ten years ago, I suppose new generation of DVD technology was invented. Now DVD can have huge capacity and this new generation of D- of DVD came in two formats. One is High Definition DVD, HD DVD, the other is Blu-ray, okay? Those two formats are incompatible. So if you have D- HD DVD player, you can't really play Blu-ray discs and the same is true or vice versa, if you have Blu-ray recorder, player, you cannot play HD DVD. Okay, so the society has at least two equilibria. In one equilibrium, everybody uses HD DVD. So here, HD DVD became de facto standard of the new generation DVD. The other equilibrium everybody uses Blu-ray, okay? So there was a struggle for de facto standard, okay. A format that happens to obtain a large enough market share eventually become de facto standard, okay? If lots of people are using Blu-ray, then you have wide range of softwares, and it's better for you to choose Blu-ray, okay. Okay, so let's see what actually happened in Japanese market. So the picture I'm going to show gives you the market shares of DVD recorders, players, HD DVD players or Blu-ray players. So initially Blu-ray was really popular, and then HD DVD was introduced, and initially it was very popular. So, this was a perfect example of the phenomenon called self-fulfilling prophecy. So you can imagine that there is a prophet saying that behold Blu-ray users, the end is near, repent and switch to HD DVD, and if everybody believes what he says, everybody buys HD DVD and HD DVD is becoming more and more desirable, and eventually people follow the prediction of this person. This is what is called self-fulfilling prophecy, but since the society has another equilibrium, Blu-ray equilibrium, there is another self-fulfilling prophecy, okay? So, if the society has multiple Nash equilibria, we have multiple self-fulfilling prophecies. So, this prophet here is saying that, hey, no- pay no attention to this stupid guy. Stick to Blu-ray, buy Blu-Ray, and let's see what actually happened, okay, eventually, people believed this guy and Blu-ray dominated the market, okay. So let me sum up. Society may have multiple Nash equilibria in this case two equilibria. Everybody uses HD DVD, everybody uses Blu-ray, and eventually Blu-ray prevailed, okay, and which one eventually prevails depends on people's expectations. So ex ante, it's really hard to predict which one eventually dominates, and also, there is no guarantee that the best format always becomes the de facto standard.
