# Yale - ECON-159 GAME THEORY Lecture 14 - Backward Induction Commitment, Spies, and First-Mover Advantages

Материал готовится,

пожалуйста, возвращайтесь позднее

пожалуйста, возвращайтесь позднее

ECON-159: GAME THEORY

Lecture 14 - Backward Induction: Commitment, Spies, and First-Mover Advantages [October 24, 2007]

Chapter 1. Sequential Games: First Mover Advantage in the Stackelberg Model [00:00:00]

Professor Ben Polak: All right, so today I want to do something a little bit more mundane than we did on Monday. I want to go back and talk about quantity competition. So in the first half of the course we talked about price competition. We talked about quantity competition. We talked about competition with differentiated products. I want to go back and revisit essentially the Cournot Model. So this was the Cournot Model: two firms are producing, are choosing their quantities simultaneously. Firm 1 is choosing Q1 and Firm 2 is choosing Q2. And all of this is just review so this is all stuff that's in your notes already. This is the demand curve. It tells us that prices depend on the total quantity being produced. So this is Q1 + Q2 and this is prices, then the demand curve is a straight line of slope b. That's what this tells us. Here's our slope –b. And we know that payoffs are just profits, which are price times quantity, revenues, minus cost times quantity, costs, we're assuming constant marginal costs.

We did this model out in full in maybe the third week of class and we figured out what the best response diagram looked like. And if you remember correctly, this was the best response for Firm 1 taking Firm 2's output as given, and this is the best response for Firm 2 taking Firm 1's output as given, and there were a few other details in here. This was the monopoly quantity, this was the competitive quantity and so on, but this is enough for today. Actually, we had done a bit more than that, we'd actually worked out in class what the equations were for these best responses. Here they are. I'm not going to re-derive these today, but they're somewhere in your notes. We kind of crunched through some calculus and figured out what Firm 1's best response looks like algebraically, here it is. So this is the equation of this line, and similarly for Firm 2, so this is the equation of this line.

Finally, we figured out what the Nash Equilibrium was, and there's no prizes here: the Nash Equilibrium in Cournot was where these best responses crossed, and this is the equation for the Nash Equilibrium. Have I made a mistake? The best response, oh thank you. The best response for Firm 1 is a function of Q2, exactly. Thanks Jake. So this is all stuff we did before, I want to go back to this model now to revisit it in the context of thinking about sequential dynamic games. So what we're going to do is — we're going to do is, we're going to imagine that rather than having these firms choose their quantities simultaneously, one firm gets to move first and the other firm moves after. Let's be clear, we're going to assume that Firm 1s moving first and the other firm — we'll assume Firm 1's going to move first — the other firm, Firm 2, is going to get observe what Firm 1 has chosen and then get to make her choice.

So we're going to see what difference it makes when we go from this classic simultaneous move game into a sequential move game. This model is fairly famous and I'm almost certainly spelling this wrong, but it's due to a guy called Stackelberg. So what we're looking at now is the Stackelberg Model. So how do we want to think about this?

Lecture 14 - Backward Induction: Commitment, Spies, and First-Mover Advantages [October 24, 2007]

Chapter 1. Sequential Games: First Mover Advantage in the Stackelberg Model [00:00:00]

Professor Ben Polak: All right, so today I want to do something a little bit more mundane than we did on Monday. I want to go back and talk about quantity competition. So in the first half of the course we talked about price competition. We talked about quantity competition. We talked about competition with differentiated products. I want to go back and revisit essentially the Cournot Model. So this was the Cournot Model: two firms are producing, are choosing their quantities simultaneously. Firm 1 is choosing Q1 and Firm 2 is choosing Q2. And all of this is just review so this is all stuff that's in your notes already. This is the demand curve. It tells us that prices depend on the total quantity being produced. So this is Q1 + Q2 and this is prices, then the demand curve is a straight line of slope b. That's what this tells us. Here's our slope –b. And we know that payoffs are just profits, which are price times quantity, revenues, minus cost times quantity, costs, we're assuming constant marginal costs.

We did this model out in full in maybe the third week of class and we figured out what the best response diagram looked like. And if you remember correctly, this was the best response for Firm 1 taking Firm 2's output as given, and this is the best response for Firm 2 taking Firm 1's output as given, and there were a few other details in here. This was the monopoly quantity, this was the competitive quantity and so on, but this is enough for today. Actually, we had done a bit more than that, we'd actually worked out in class what the equations were for these best responses. Here they are. I'm not going to re-derive these today, but they're somewhere in your notes. We kind of crunched through some calculus and figured out what Firm 1's best response looks like algebraically, here it is. So this is the equation of this line, and similarly for Firm 2, so this is the equation of this line.

Finally, we figured out what the Nash Equilibrium was, and there's no prizes here: the Nash Equilibrium in Cournot was where these best responses crossed, and this is the equation for the Nash Equilibrium. Have I made a mistake? The best response, oh thank you. The best response for Firm 1 is a function of Q2, exactly. Thanks Jake. So this is all stuff we did before, I want to go back to this model now to revisit it in the context of thinking about sequential dynamic games. So what we're going to do is — we're going to do is, we're going to imagine that rather than having these firms choose their quantities simultaneously, one firm gets to move first and the other firm moves after. Let's be clear, we're going to assume that Firm 1s moving first and the other firm — we'll assume Firm 1's going to move first — the other firm, Firm 2, is going to get observe what Firm 1 has chosen and then get to make her choice.

So we're going to see what difference it makes when we go from this classic simultaneous move game into a sequential move game. This model is fairly famous and I'm almost certainly spelling this wrong, but it's due to a guy called Stackelberg. So what we're looking at now is the Stackelberg Model. So how do we want to think about this?

Загрузка...

Выбрать следующее задание

Ты добавил

Выбрать следующее задание

Ты добавил