Question 1

The figure below presents information for a one-shot game. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text { Low  Price } & \text { High Price } \
\hline \text { Low  Price } & (2,2) & (10,-8) \
\hline \text { HighPrice } & (-8,10) & (6,6) \
\hline
\end{array}\end{array}$ What are secure strategies for firm A and firm B respectively?
A) (low price, high price)
B) (high price, low price)
C) (high price, high price)
D) (low price, low price)

Accepted Answer

D

Question 2

If you advertise and your rival advertises,you each will earn $4 million in profits.If neither of you advertises,you will each earn $10 million in profits.However,if one of you advertises and the other does not,the firm that advertises will earn $1 million and the non-advertising firm will earn $5 million.If you and your rival plan to be in business for only one year,the Nash equilibrium is:
A) for each firm to advertise.
B) for neither firm to advertise.
C) for your firm to advertise and the other not to advertise.
D) None of the preceding answers is correct.

Accepted Answer

The Nash equilibrium is for neither firm to advertise because each firm earns $10 million in profits if neither advertises, but only $4 million in profits if both advertise.

Question 3

Consider the following entry game: Here,firm B is an existing firm in the market,and firm A is a potential entrant.Firm A must decide whether to enter the market (play "enter")or stay out of the market (play "not enter").If firm A decides to enter the market,firm B must decide whether to engage in a price war (play "hard"),or not (play "soft").By playing "hard," firm B ensures that firm A makes a loss of $1 million,but firm B only makes $1 million in profits.On the other hand,if firm B plays "soft," the new entrant takes half of the market,and each firm earns profits of $5 million.If firm A stays out,it earns zero while firm B earns $10 million.Which of the following are perfect equilibrium strategies?
A) (enter, soft)
B) (not enter, soft)
C) (enter, hard)
D) (not enter, hard)

Accepted Answer

If firm A stays out, firm B earns $10 million, which is better than the $1 million from playing "hard" or $5 million from playing "soft" if firm A enters. Therefore, firm B's best response to firm A not entering is irrelevant, and firm A's best strategy is not to enter, making (not enter, hard) a perfect equilibrium.

Question 4

Refer to the following game. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text {Low   Price } & \text { High Price } \
\hline \text {Low  Price } & (10,9) & (15,8) \
\hline \text { High  Price } & (-10,7) & (11,11) \
\hline
\end{array}\end{array}$ If this one-shot game is repeated three times,the Nash equilibrium payoffs for firms A and B will be ______ each period.
A) (10, 9)
B) (11, 11)
C) (?10, 7)
D) (15, 8)

Accepted Answer

The answer of Refer to the following game. \(\begin{array}{l}
\quad\quad\quad\quad\quad\text {...

Question 5

In the game shown below,firms 1 and 2 must independently decide whether to charge high or low prices. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm Two }\
\text { Firm One }
\begin{array}{|l|l|l|}
\hline & \text { High Price } & \text { Low Price } \
\hline \text { High Price } & (10,10) & (5,-5) \
\hline \text { Low Price } & (5,-5) & (0,0) \
\hline
\end{array}\end{array}$ Which of the following are the Nash equilibrium payoffs (each period)if the game is repeated 10 times?
A) (0, 0)
B) (5, -5)
C) (-5, 5)
D) (10, 10)

Accepted Answer

In a repeated game, the Nash equilibrium can be defined as a strategy profile that is a Nash equilibrium in every subgame of the repeated game, including the last period. In this game, the only Nash equilibrium is for both firms to choose the high price in every period, resulting in a payoff of (10,10) in every period. This strategy profile is a Nash equilibrium because neither firm has an incentive to deviate to the low price in any period, as doing so would result in a lower payoff in that period and may cause the other firm to retaliate with a low price in future periods, leading to even lower payoffs in the long run. Therefore, the Nash equilibrium payoff in every period is (10,10).

Question 6

Which of the following are important determinants of collusion in pricing games?
A) The number of firms
B) Firm size
C) History
D) All of the statements associated with this question are correct.

Accepted Answer

All of the statements are important determinants of collusion in pricing games. The number of firms affects the difficulty of collusion, as it is easier for a small number of firms to coordinate and reach agreements. Firm size may also play a role, as larger firms may have more market power and a greater ability to enforce agreements. History is important because past collusion behavior can signal to other firms the likelihood of future collusion.

Question 7

In the game shown below,firms 1 and 2 must independently decide whether to charge high or low prices. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm Two }\
\text { Firm One }
\begin{array}{|l|l|l|}
\hline & \text { High Price } & \text { Low Price } \
\hline \text { High Price } & (10,10) & (5,-5) \
\hline \text { Low Price } & (5,-5) & (0,0) \
\hline
\end{array}\end{array}$ Which of the following are Nash equilibrium payoffs in the one-shot game?
A) (0, 0)
B) (5, -5)
C) (-5, 5)
D) (10, 10)

Accepted Answer

A Nash equilibrium occurs when each player’s strategy is a best response to the other player’s strategy. Firm one will not deviate from charging a high price given that if it charges a low price, firm two charging a high price gives firm one a payoff of 5 whereas firm one charging a low price gives firm one a payoff of 0. Firm two will not deviate from charging a high price given that if it charges a low price, firm one charging a high price gives firm two a payoff of 5 whereas firm one charging a low price gives firm two a payoff of -5. Thus, (10,10) is a Nash equilibrium payoff.

Question 8

Refer to the following game. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text {Low   Price } & \text { High Price } \
\hline \text {Low  Price } & (10,9) & (15,8) \
\hline \text { High  Price } & (-10,7) & (11,11) \
\hline
\end{array}\end{array}$ What are the secure strategies for firm A and firm B respectively?
A) (low price, high price)
B) (high price, low price)
C) (high price, high price)
D) (low price, low price)

Accepted Answer

Firm A's secure strategy is to play low price, regardless of what firm B does. Firm B's secure strategy is to play high price, regardless of what firm A does.

Question 9

In the game shown below,firms 1 and 2 must independently decide whether to charge high or low prices. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm Two }\
\text { Firm One }
\begin{array}{|l|l|l|}
\hline & \text { High Price } & \text { Low Price } \
\hline \text { High Price } & (10,10) & (5,-5) \
\hline \text { Low Price } & (5,-5) & (0,0) \
\hline
\end{array}\end{array}$ Suppose the game is infinitely repeated.Then the "best" the firms could do in a Nash equilibrium is to earn ___ per period.
A) (0, 0)
B) (5, -5)
C) (-5, 5)
D) (10, 10)

Accepted Answer

In an infinitely repeated game, firms can sustain cooperation to avoid the temptation of undercutting each other. By both charging high prices, they can achieve the (10, 10) outcome each period, which is the best they can do while maintaining a Nash equilibrium. This relies on the threat of reverting to a less favorable outcome if one cheats, ensuring mutual best response.

Question 10

Consider the following information for a simultaneous move game: If you advertise and your rival advertises,you each will earn $5 million in profits.If neither of you advertises,you will each earn $10 million in profits.However,if one of you advertises and the other does not,the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million.If you and your rival plan to be in business for 10 years,then the Nash equilibrium is:
A) for each firm to advertise every year.
B) for neither firm to advertise in early years, but to advertise in later years.
C) for each firm to not advertise in any year.
D) for each firm to advertise in early years, but not advertise in later years.

Accepted Answer

In a Nash equilibrium, each player's strategy is optimal given the other player's strategy. Here, advertising always yields a better outcome for a firm regardless of the rival's action ($5 million if both advertise, $15 million if only one advertises) compared to not advertising ($10 million if neither advertises, $1 million if the rival advertises). Thus, the equilibrium is for both to advertise every year to ensure they do not end up with the worst outcome of $1 million.

Question 11

Refer to the following game. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text {Low   Price } & \text { High Price } \
\hline \text {Low  Price } & (10,9) & (15,8) \
\hline \text { High  Price } & (-10,7) & (11,11) \
\hline
\end{array}\end{array}$ Which of the following is true?
A) A dominant strategy for firm A is "high price."
B) There does not exist a dominant strategy for firm A.
C) A dominant strategy for firm B is "low price."
D) None of the preceding answers is correct.

Accepted Answer

There is no dominant strategy for either firm A or B. A dominant strategy is a strategy that is the best choice for a player regardless of what their opponent chooses. In this game, whether firm A chooses a low or high price, the best choice for firm B depends on what A chooses. Similarly, whether firm B chooses a low or high price, the best choice for firm A depends on what B chooses. Therefore, there is no dominant strategy for either firm.

Question 12

The figure below presents information for a one-shot game. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text { Low  Price } & \text { High Price } \
\hline \text { Low  Price } & (2,2) & (10,-8) \
\hline \text { HighPrice } & (-8,10) & (6,6) \
\hline
\end{array}\end{array}$ If this one-shot game is repeated 100 times,the Nash equilibrium payoffs of the players will be ________________ each period.
A) (2, 2)
B) (10, ?8)
C) (?8, 10)
D) (6, 6)

Accepted Answer

The Nash equilibrium of a one-shot game is the strategy profile that maximizes each player's payoff given the strategies of the other players. In this game, the Nash equilibrium is for both players to choose the Low Price strategy. This is because if Firm A chooses the Low Price strategy, Firm B will also choose the Low Price strategy to maximize its payoff. Similarly, if Firm A chooses the High Price strategy, Firm B will also choose the Low Price strategy to maximize its payoff. Therefore, the Nash equilibrium payoffs of the players will be (2, 2) each period.

Question 13

If you advertise and your rival advertises,you each will earn $4 million in profits.If neither of you advertises,you will each earn $10 million in profits.However,if one of you advertises and the other does not,the firm that advertises will earn $1 million and the non-advertising firm will earn $5 million.If you and your rival plan to be in business for 10 years,then the Nash equilibrium is:
A) for each firm to advertise every year.
B) for neither firm to advertise in early years, but to advertise in later years.
C) for each firm to not advertise in any year.
D) for each firm to advertise in early years, but not advertise in later years.

Accepted Answer

The Nash equilibrium is the scenario where neither firm advertises in any year. This is because if one firm advertises and the other does not, the non-advertising firm earns a higher profit ($5 million) than the advertising firm ($1 million). Therefore, if one firm advertises, the other firm will have an incentive to not advertise and earn a higher profit. If both firms advertise, they will earn lower profits ($4 million) than if neither of them advertise ($10 million). Thus, the Nash equilibrium is for each firm to not advertise in any year.

Question 14

Consider the following information for a simultaneous move game: If you advertise and your rival advertises,you each will earn $5 million in profits.If neither of you advertises,you will each earn $10 million in profits.However,if one of you advertises and the other does not,the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million.If you and your rival plan to hand your business down to your children (and this "bequest" goes on forever),then a Nash equilibrium when the interest rate is zero is:
A) for each firm to not advertise until the rival does, and then to advertise forever.
B) for your firm to never advertise.
C) for your firm to always advertise when your rival does.
D) for each firm to advertise until the rival does not advertise, and then not advertise forever.

Accepted Answer

When the interest rate is zero, future profits are valued equally to current profits. The strategy of not advertising until the rival does, and then advertising forever, is a Nash equilibrium because it maximizes long-term profits by maintaining the higher profit of $10 million each when neither advertises, while deterring unilateral advertising by threatening to advertise if the rival does.

Question 15

Which of the following is true?
A) In a one-shot game, a collusive strategy always represents a Nash equilibrium.
B) A perfect equilibrium occurs when each player is doing the best he can regardless of what the other player is doing.
C) Each Nash equilibrium is a perfect equilibrium.
D) Every perfect equilibrium is a Nash equilibrium.

Accepted Answer

A perfect equilibrium is a refinement of Nash equilibrium, meaning every perfect equilibrium must satisfy the conditions of a Nash equilibrium. However, not every Nash equilibrium is perfect due to issues like non-credible threats or actions in extensive-form games. Choices A and B are incorrect because a collusive strategy in a one-shot game does not always represent a Nash equilibrium due to incentives to deviate, and a perfect equilibrium specifically requires each player's strategy to be optimal given the strategies of the others, not regardless of them. Choice C is incorrect because it reverses the relationship; while every perfect equilibrium is a Nash equilibrium, not every Nash equilibrium is a perfect equilibrium.

Question 16

Refer to the following game. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text {Low   Price } & \text { High Price } \
\hline \text {Low  Price } & (10,9) & (15,8) \
\hline \text { High  Price } & (-10,7) & (11,11) \
\hline
\end{array}\end{array}$ What are the Nash equilibrium strategies for firm A and firm B,respectively,in a one-shot game?
A) (low price, low price)
B) (high price, high price)
C) (low price, high price)
D) (low price, low price) and (high price, high price)

Accepted Answer

The answer of Refer to the following game. \(\begin{array}{l}
\quad\quad\quad\quad\quad\text {...

Question 17

Consider the following information for a simultaneous move game: If you advertise and your rival advertises,you each will earn $5 million in profits.If neither of you advertises,you will each earn $10 million in profits.However,if one of you advertises and the other does not,the firm that advertises will earn $15 million and the non-advertising firm will earn $1 million.If you and your rival plan to be in business for only one year,the Nash equilibrium is:
A) for each firm to advertise.
B) for neither firm to advertise.
C) for your firm to advertise and the other not to advertise.
D) None of the preceding answers is correct.

Accepted Answer

In a Nash equilibrium, each player's strategy is optimal given the other player's strategy. Here, advertising is a dominant strategy for both firms because it guarantees a higher payoff ($5 million or $15 million) regardless of the other firm's action, compared to not advertising ($10 million or $1 million). Thus, the Nash equilibrium is for both firms to advertise.

Question 18

Consider the following entry game: Here,firm B is an existing firm in the market,and firm A is a potential entrant.Firm A must decide whether to enter the market (play "enter")or stay out of the market (play "not enter").If firm A decides to enter the market,firm B must decide whether to engage in a price war (play "hard"),or not (play "soft").By playing "hard," firm B ensures that firm A makes a loss of $1 million,but firm B only makes $1 million in profits.On the other hand,if firm B plays "soft,",the new entrant takes half of the market,and each firm earns profits of $5 million.If firm A stays out,it earns zero while firm B earns $10 million.Which of the following are Nash equilibrium strategies?
A) (enter, hard) and (not enter, hard)
B) (enter, soft) and (not enter, soft)
C) (not enter, hard) and (enter, soft)
D) (enter, hard) and (not enter, soft)

Accepted Answer

A Nash equilibrium occurs when no player can benefit by changing their strategy while the other players keep theirs unchanged. In this scenario, "(not enter, hard)" is a Nash equilibrium because if Firm A doesn't enter, its best response is to earn zero (since entering would result in a loss if B plays hard), and Firm B's best response to A not entering is to play hard, maximizing its profit at $10 million. Similarly, "(enter, soft)" is a Nash equilibrium because if Firm A enters, Firm B's best response is to play soft, allowing both to earn $5 million, and Firm A's best response to B playing soft is to enter, as it earns more than not entering ($5 million vs. $0).

Question 19

If you advertise and your rival advertises,you each will earn $4 million in profits.If neither of you advertises,you will each earn $10 million in profits.However,if one of you advertises and the other does not,the firm that advertises will earn $1 million and the non-advertising firm will earn $5 million.If you and your rival plan to hand your business down to your children (and this "bequest" goes on forever),then a Nash equilibrium is for each firm to:
A) not advertise until the rival does, and then to advertise forever.
B) never advertise.
C) always advertise.
D) advertise until the rival does not advertise, and then not advertise forever.

Accepted Answer

In this scenario, the Nash equilibrium is for both firms to never advertise. This is because if both firms choose not to advertise, they each earn the highest possible profit of $10 million. Any deviation from this strategy (i.e., choosing to advertise) would result in a lower profit for the deviating firm, making it an undesirable choice. This setup ensures that not advertising is the best response for each firm, regardless of the other firm's decision, fulfilling the criteria for a Nash equilibrium.

Question 20

The figure below presents information for a one-shot game. $\begin{array}{l}
\quad\quad\quad\quad\quad\text { Firm B }\
\text { Firm A}
\begin{array}{|l|l|l|}
\hline & \text { Low  Price } & \text { High Price } \
\hline \text { Low  Price } & (2,2) & (10,-8) \
\hline \text { HighPrice } & (-8,10) & (6,6) \
\hline
\end{array}\end{array}$ What are the Nash equilibrium strategies for firm A and B respectively?
A) (low price, high price)
B) (high price, low price)
C) (high price, high price)
D) (low price, low price)

Accepted Answer

The answer of The figure below presents information for a...

Quiz 10: Game Theory: Inside Oligopoly

Which of the following are important determinants of collusion in pricing games?

Which of the following is true?