Chapter 12R, Problem 2FRQ

a)

To determine

The question requires us to find a dominant strategy if the firm has one.

Answer to Problem 2FRQ

Big Bubble Co. doesn’t have a dominant strategy.

Explanation of Solution

There are two players in this game:

• Big Bubble Co.
• Long Lasting Flavor Co.

They are facing the payoffs to choose between set higher prices and setting the lower price.

In the given game, none of the players have a dominant strategy as they are not choosing the same payoffs irrespective of what the opponent has done.

1. If firm B chooses a high price to set, then Nash strategy for firm L is to set a lower price as firm L is getting a higher return.
2. If firm B chooses a low price to set, then Nash strategy for firm L is to set a higher price as firm L is getting a higher return.
3. If firm L chooses a high price to set, then Nash strategy for firm B is to set a lower price as firm B is getting a higher return.
4. If firm L chooses a low price to set, then Nash strategy for firm B is to set a higher price as firm B is getting a higher return.

Here, both firms are changing their Nash strategy considering the payoffs chosen by their opponents. They do not stick to the same payoffs during the game.

Therefore, Big Bubble Co. doesn’t have a dominant strategy.

Economics Concept Introduction

A firm will have a dominant strategy when it chooses the same payoffs irrespective of what the other player has done.

b)

To determine

The question requires us to find a dominant strategy if the firm has one.

Answer to Problem 2FRQ

Long Lasting Flavor Co. doesn’t have a dominant strategy.

Explanation of Solution

In the given game, none of the players have a dominant strategy as they are not choosing the same payoffs irrespective of what the opponent has done.

1. If firm B chooses a high price to set, then Nash strategy for firm L is to set a lower price as firm L is getting a higher return.
2. If firm B chooses a low price to set, then Nash strategy for firm L is to set a higher price as firm L is getting a higher return.
3. If firm L chooses a high price to set, then Nash strategy for firm B is to set a lower price as firm B is getting a higher return.
4. If firm L chooses a low price to set, then Nash strategy for firm B is to set a higher price as firm B is getting a higher return.

Here, both firms are changing their Nash strategy considering the payoffs chosen by their opponents. They do not stick to the same payoffs during the game.

Therefore, Long Lasting Flavor Co. doesn’t have a dominant strategy.

Economics Concept Introduction

A firm will have a dominant strategy when it chooses the same payoffs irrespective of what the other player has done.

c)

To determine

The question requires us to find the Nash equilibrium if the firm has one.

Explanation of Solution

In the given game, there are two Nash equilibria:

1. (set higher price, set lower price)
2. (set lower price, set higher price)

As per the given explanation in part “a” and part “b”, firms’ Nash strategies match given a nash equilibrium if both choose to set a higher price.

Similarly, the Nash strategies also match if both choose to set the lower price because given one of them has chosen to set a higher price, the best strategy for another is to set the lower price.

Therefore, firms have two nash equilibria in this game.

Economics Concept Introduction

Nash equilibrium is a situation when nash strategies of the firms match i,e, both the firms are doing the best they can given what other players are doing.