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ECON-159: GAME THEORY

Lecture 7 - Nash Equilibrium: Shopping, Standing and Voting on a Line [September 26, 2007]

Chapter 1. Bertrand Duopoly: Standard Model [00:00:00]

Professor Ben Polak: All right, so last time we started to study imperfect competition. We looked at the Cournot model, but the bigger theme is the study of how firms compete outside of the sort of easy cases that you study in 115: so outside of the example of monopoly, where there is only one firm and so there's not much competition; and outside the case of perfect competition where there are so many firms, it's as if each firm is a price taker. We're going to continue with that today, and in fact you're going to continue with it on into the homework.

So last time, we looked at Cournot. It was the model we started with. We looked at two firms competing in quantities. And just to review a little bit what we did last time, the kind of exercise there — so I think, is this right, I think probably went a little fast last time. I was kicking myself afterwards. People can nod or shake their heads. I think I went a bit fast, so I'm sorry for that. If there was a time to go too fast it was probably last time, because it turns out this is something that's covered well in the textbook, so it's covered in chapter six of the textbook. But the kind of exercise we did last time is a useful exercise for those of you who are Econ majors.

The way we solved that Cournot model was we did three kinds of things. We did something very nerdy, namely, we just played with calculus and algebra. That was sort of mathy. We did something a little bit less nerdy, that is, we drew some pictures that represented what we'd found. And we did a third thing, which we tried to match this up to the economic intuition about monopoly, and perfect competition, and demand curves, and so on. And this exercise of being able to work in these three different modes, economic intuition, graphs, and kind of nerdy high school math is a lot of what we want to get you used to as Economic Majors, just to be able to translate easily between those.

Again, I apologize for going too fast but it's still a useful exercise I think, so have a look at it in the book. Now back to the lessons and away from the nerdiness a second, what did we learn? Well at the end of the day we learned that in the Cournot Equilibrium, things were, as we perhaps might have anticipated — things sat naturally between the extreme cases. So the amount of output produced by the industry was somewhere between the case that would be under monopoly and under perfect competition. It was more than under monopoly, less than perfect competition. Prices in the industry, if we'd gone back and checked, would sit between. They would be lower than the monopoly prices, but higher than the perfect competitive prices.

Industry profits would be in between. Industry profits would be less than monopoly. They must be less than monopoly, since that's the highest they could ever be. And they're higher than perfect competition, which of course, has zero profits in this case. Consumer surplus, the benefits flowing to consumers lie in between. So in fact the model, in addition to the sort of nerdiness of the model, it ended up with a result we kind of believe in. If you have imperfect competition, it's somewhere between perfect competition and no competition. But, what's the "but"?

Lecture 7 - Nash Equilibrium: Shopping, Standing and Voting on a Line [September 26, 2007]

Chapter 1. Bertrand Duopoly: Standard Model [00:00:00]

Professor Ben Polak: All right, so last time we started to study imperfect competition. We looked at the Cournot model, but the bigger theme is the study of how firms compete outside of the sort of easy cases that you study in 115: so outside of the example of monopoly, where there is only one firm and so there's not much competition; and outside the case of perfect competition where there are so many firms, it's as if each firm is a price taker. We're going to continue with that today, and in fact you're going to continue with it on into the homework.

So last time, we looked at Cournot. It was the model we started with. We looked at two firms competing in quantities. And just to review a little bit what we did last time, the kind of exercise there — so I think, is this right, I think probably went a little fast last time. I was kicking myself afterwards. People can nod or shake their heads. I think I went a bit fast, so I'm sorry for that. If there was a time to go too fast it was probably last time, because it turns out this is something that's covered well in the textbook, so it's covered in chapter six of the textbook. But the kind of exercise we did last time is a useful exercise for those of you who are Econ majors.

The way we solved that Cournot model was we did three kinds of things. We did something very nerdy, namely, we just played with calculus and algebra. That was sort of mathy. We did something a little bit less nerdy, that is, we drew some pictures that represented what we'd found. And we did a third thing, which we tried to match this up to the economic intuition about monopoly, and perfect competition, and demand curves, and so on. And this exercise of being able to work in these three different modes, economic intuition, graphs, and kind of nerdy high school math is a lot of what we want to get you used to as Economic Majors, just to be able to translate easily between those.

Again, I apologize for going too fast but it's still a useful exercise I think, so have a look at it in the book. Now back to the lessons and away from the nerdiness a second, what did we learn? Well at the end of the day we learned that in the Cournot Equilibrium, things were, as we perhaps might have anticipated — things sat naturally between the extreme cases. So the amount of output produced by the industry was somewhere between the case that would be under monopoly and under perfect competition. It was more than under monopoly, less than perfect competition. Prices in the industry, if we'd gone back and checked, would sit between. They would be lower than the monopoly prices, but higher than the perfect competitive prices.

Industry profits would be in between. Industry profits would be less than monopoly. They must be less than monopoly, since that's the highest they could ever be. And they're higher than perfect competition, which of course, has zero profits in this case. Consumer surplus, the benefits flowing to consumers lie in between. So in fact the model, in addition to the sort of nerdiness of the model, it ended up with a result we kind of believe in. If you have imperfect competition, it's somewhere between perfect competition and no competition. But, what's the "but"?

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