Chapter 65, Problem 2FRQ

a)

To determine

The payoff matrix for the game by filling each of the payoffs.

Explanation of Solution

The following payoff matrix for this game shows each pay-off where firm A is mentioned on the left side and firm B is on the upside.

Here, the firms’ profit is in millions of dollars.

L Firm A H	Firm B  L    H
	($2, $2)	($4, $1)
	($1, $4)	($3, $3)

Economics Concept Introduction

Introduction: The payoff matrix is that which is just a double-entry table and it lists every payment made by one participant to the other for each accepted strategy.

b)

To determine

The dominant strategy for each player

Explanation of Solution

Yes, there is a dominating strategy when one firm chooses low prices because consumers will move to that firm that offers them a low or expected price of goods in the market which reduces the profits of other firms in the market. Therefore, the dominant strategy for one firm from both will exist when they get high returns or profits by charging low prices than other firms in the market as it decreases the profit of others.

Economics Concept Introduction

Introduction: A situation where one player considers superior strategies without knowing the impact of how these strategies will influence the opponent to play refers to the dominating strategy.

c)

To determine

The Nash equilibrium in the game

Explanation of Solution

Both firms can have Nash equilibrium in this game because one firm such as firm A will not be motivated to change if firm B selects low and if firm A selects high ($4 > $1 for Firm B and $1<$4 for Firm B). Game Similarly, if firm B selects a high price then firm A selects a low, and neither will be motivated to alter, therefore, the profits will become high for one and low for another ($4 > $1 for Firm A and $1 < $4 for Firm B).

Therefore, two results are Nash equilibriums.

Economics Concept Introduction

Introduction: Nash equilibrium is a state in which a player can attain the desired result by sticking to their starting approach.

d)

To determine

The new payoff matrix with adjustments by supposing a tax on high-priced goods which causes a $500,000 decrease in the payoffs of a high price

Explanation of Solution

The new pay-off matrix will be seen as follows where the tax rate cut the profit of both firms.

Here, the firms’ profit is in millions of dollars.

L Firm A H	Firm B  L   H
	($2, $2)	($3.5, $1)
	($1, $3.5)	($2.5, $2.5)

Economics Concept Introduction

Introduction: The payoff matrix is that which is just a double-entry table and it lists every payment made by one participant to the other for each accepted strategy.