Question 1

Nash equilibria are stable because
A) they involve dominant strategies.
B) they involve constant-sum games.
C) they occur in noncooperative games.
D) once the strategies are chosen, no players have an incentive to negotiate jointly to change them.
E) once the strategies are chosen, no player has an incentive to deviate unilaterally from them.

Accepted Answer

The answer of Nash equilibria are stable because
A) they involve...

Question 2

Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs:

What are the dominant strategies in this game?
A) Both firms produce low levels of output
B) Both firms produce high levels of output
C) Firm A's dominant strategy is to produce low levels of output, but Firm B does not have a dominant strategy.
D) Firm B's dominant strategy is to produce low levels of output, but Firm A does not have a dominant strategy.
E) Neither firm has a dominant strategy

Accepted Answer

The answer of Consider the following game in which two...

Question 3

Andre Agassi, a star tennis player, is playing the number one player in the world, Roger Federer. Before the match, Agassi decided that he would serve 20 percent of his serves to Federer's backhand, 30 percent of his serves to Federer's forehand, and 50 percent of his serves straight at Federer. In the language of game theory, this is known as:
A) a pure strategy.
B) a dominant strategy.
C) a mixed strategy.
D) a maximin strategy.

Accepted Answer

Agassi's decision to serve to Federer's backhand, forehand, or straight at him is a mixed strategy because it involves a randomization of his choices based on a predetermined mix. Agassi's goal is to keep Federer guessing and prevent him from anticipating his serves, which can give Agassi an advantage in the match. A pure strategy would involve choosing one specific option every time, while a dominant strategy would involve choosing the same option regardless of the opponent's actions. A maximin strategy would involve choosing the option with the highest minimum payoff. None of these other strategies accurately describe Agassi's approach to serving.

Question 4

The relationship between a pure-strategy Nash equilibrium and a dominant-strategy equilibrium is that
A) a dominant-strategy equilibrium is a special case of a pure-strategy Nash equilibrium.
B) a pure-strategy Nash equilibrium is a special case of a dominant-strategy equilibrium.
C) they are the same.
D) there may not be a dominant-strategy equilibrium, but there always is a pure-strategy Nash equilibrium.
E) they are mutually exclusive and exhaustive, in that a dominant-strategy equilibrium is the same thing as a mixed-strategy Nash equilibrium.

Accepted Answer

A dominant-strategy equilibrium is a special case of a pure-strategy Nash equilibrium, meaning that if a dominant strategy exists, it will be played by both players in a Nash equilibrium. However, there may be instances where a pure-strategy Nash equilibrium exists without a dominant strategy, so option D is not correct. Option B and E are incorrect because they imply that a dominant-strategy equilibrium is a broader or equivalent concept to a pure-strategy Nash equilibrium, which is not the case. Option C is also incorrect since it oversimplifies the relationship between the two concepts.

Question 5

Scenario 13.5
Consider the following game: 
-Which of the following is true regarding the game in Scenario 13.5?
A) Only Bull Meat has a dominant strategy.
B) Only Deer Meat has a dominant strategy.
C) Both companies have a dominant strategy: expand West.
D) Both companies have a dominant strategy: expand South.
E) Neither company has a dominant strategy.

Accepted Answer

From the given information, it is not possible to determine any dominant strategy for either Bull Meat or Deer Meat. Therefore, neither company has a dominant strategy, and the answer is E.

Question 6

A Nash equilibrium occurs when
A) each firm is doing the best it can given its opponents' actions.
B) each firm chooses the strategy that maximizes its minimum gain.
C) a player can choose a strategy that is optimal regardless of its rivals' actions.
D) there is no dominant firm in a market.

Accepted Answer

A Nash equilibrium occurs when each firm is doing the best it can given its opponents' actions. In other words, no firm can improve its own payoff by unilaterally changing its strategy while its competitors keep their strategies unchanged. This is the key concept of game theory and the Nash equilibrium is the most stable outcome in a game.

Question 7

Use the following statements to answer this question:
I. If mixed strategies are allowed, every game has at least one Nash equilibrium.
II. The maximin strategy is optimal in the game of "matching pennies."
A) Both I and II are true.
B) I is true, and II is false.
C) I is false, and II is true.
D) Both I and II are false.

Accepted Answer

I is true because according to Nash's theorem, every finite game has at least one Nash equilibrium, which may involve mixed strategies. II is false because in "matching pennies," the maximin strategy is not optimal; the game is zero-sum and involves pure strategy Nash equilibria, not a maximin approach.

Question 8

Scenario 13.6
Consider the following game. Payoffs are in millions of dollars. 
-In the game in Scenario 13.6,
A) "Poison Pill" is a dominant strategy for Lawrence LLP.
B) "Dump" is a dominant strategy for Lawrence LLP.
C) "TurboTech" is a dominant strategy for ERS Co.
D) "ZamboniTech" is a dominant strategy for ERS Co.
E) No firm has a dominant strategy.

Accepted Answer

The answer of Scenario 13.6
Consider the following game. Payoffs are...

Question 9

Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs:

What is the Nash equilibrium for this game?
A) Both firms producer low levels of output
B) Both firms produce high levels of output
C) Firm A produces low levels of output, and Firm B produces high output.
D) Firm A produces high levels of output, and Firm B produces low output.
E) There is more than one Nash equilibrium for this game

Accepted Answer

The answer of Consider the following game in which two...

Question 10

A maximin strategy
A) maximizes the minimum gain that can be earned.
B) maximizes the gain of one player, but minimizes the gain of the opponent.
C) minimizes the maximum gain that can be earned.
D) involves a random choice between two strategies, one which maximizes potential gain and one which minimizes potential loss.

Accepted Answer

A maximin strategy is a decision-making process that maximizes the minimum outcome or minimizes the maximum loss. It is the best choice because it focuses on ensuring the best possible outcome by minimizing the risk of loss.

Question 11

Scenario 13.6
Consider the following game. Payoffs are in millions of dollars. 
-In the game in Scenario 13.6, what is the Nash equilibrium?
A) The strategy pair associated with -$100, -$1.
B) The strategy pair associated with $2, -$0.5.
C) The strategy pair associated with $1, -$1.
D) The strategy pair associated with -$0.5, -$0.5.
E) There is no Nash equilibrium in pure strategies.

Accepted Answer

In a Nash equilibrium, neither player has an incentive to deviate from their strategy given the other player's strategy. In this game, we can see that if row chooses strategy A, column's best response is to choose strategy X, which gives a payoff of $2. However, if row chooses strategy B, column's best response is to choose strategy Y, which gives a payoff of -$0.5. Since row's payoff is higher with strategy A than with strategy B and column's payoff is higher with strategy X than with strategy Y, neither player has an incentive to deviate. Therefore, the Nash equilibrium is the strategy pair associated with $2, -$0.5.

Question 12

Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs:

What are the dominant strategies in this game?
A) Both firms produce low levels of output
B) Both firms produce high levels of output
C) Firm A's dominant strategy is to produce low levels of output, but Firm B does not have a dominant strategy.
D) Firm B's dominant strategy is to produce low levels of output, but Firm A does not have a dominant strategy.
E) Neither firm has a dominant strategy

Accepted Answer

The answer of Consider the following game in which two...

Question 13

In the game in Scenario 13.5,
A) there is one equilibrium: for both to expand West.
B) there is one equilibrium: for both to expand South.
C) there are two equilibria: either can expand in the West, and the other expands in the South.
D) there is only a mixed strategies equilibrium.
E) all four outcomes are equilibria.

Accepted Answer

Both players have a dominant strategy to expand west. However, if one player chooses to expand south, then the other player has an incentive to also expand south in order to capture more territory. Therefore, there are two equilibria: either both players expand west, or one player expands west while the other expands south.

Question 14

Scenario 13.4
Consider the following game: 
-In the game in Scenario 13.4, the equilibrium outcome:
A) is for both NRG and Vita to sponsor the marathon.
B) is for both NRG and Vita to sponsor the TV show.
C) is for NRG to sponsor the marathon and Vita to sponsor the TV show.
D) is for NRG to sponsor the TV show and Vita to sponsor the marathon.
E) does not exist in pure strategies.

Accepted Answer

The answer of Scenario 13.4
Consider the following game: 
-In the...

Question 15

If both players in a game have dominant strategies, we say that the game has:
A) a constant sum.
B) a nonconstant sum.
C) independence of irrelevant alternatives.
D) an equilibrium in dominant strategies.

Accepted Answer

If both players have dominant strategies, it means that regardless of what the other player does, they will always choose the same strategy. This results in an equilibrium in dominant strategies, where both players are making the best decision for themselves based on their dominant strategy.

Question 16

In a Nash equilibrium,
A) each player has a dominant strategy.
B) no players have a dominant strategy.
C) at least one player has a dominant strategy.
D) players may or may not have dominant strategies.
E) the player with the dominant strategy will win.

Accepted Answer

In a Nash equilibrium, players may or may not have dominant strategies. A Nash equilibrium is a situation in which each player is doing the best they can given the choices of the other players. It is possible for players to have dominant strategies in a Nash equilibrium, but it is not a necessary condition. Players may also choose non-dominant strategies that are still optimal given the choices of the other players.

Question 17

Scenario 13.6
Consider the following game. Payoffs are in millions of dollars. 
-Refer to the game in Scenario 13.6. What will occur if ERS Co. plays a maximin strategy?
A) -$100, -$1
B) $2, -$0.5
C) $1, -$1
D) -$0.5, -$0.5
E) There is a 0.25 chance of each outcome in that case.

Accepted Answer

A maximin strategy involves choosing the action that maximizes the minimum payoff achievable. In this scenario, choosing the option that ensures the least negative outcome for ERS Co. would result in a payoff of -$0.5 for both parties, which corresponds to option D.

Question 18

Scenario 13.7:
Consider the game below about funding and construction of a dam to protect a 1,000-person town. Contributions to the Dam Fund, once made, cannot be recovered, and all citizens must contribute $1,000 to the dam in order for it to be built. The dam, if built, is worth $70,000 to each citizen. 
-In the game in Scenario 13.7, the strategy pair that pays
A) $69,000 to each player is the only equilibrium.
B) ($0, -$1000) is the only equilibrium.
C) (-$1000, $0) is the only equilibrium.
D) $0 to each player is the only equilibrium.
E) $69,000 to each player and the strategy pair that pays $0 to each player are equilibria.

Accepted Answer

The only equilibrium in this game is where both players contribute to the Dam Fund and the dam is built, resulting in a pay-off of $69,000 to each player. However, the strategy pair that results in $0 pay-off to each player is also an equilibrium, but not the only one. Therefore, the best choice is to contribute to the Dam Fund and build the dam, resulting in a pay-off of $69,000 to each player.

Question 19

BuyRight is a chain of grocery stores operating in small cities throughout the southwestern United States. BuyRight's major competition comes from another chain, Acme Food Stores. Both firms are currently contemplating their advertising strategy for the region. The possible outcomes are illustrated by the payoff matrix below.  
Entries in the payoff matrix are profits. BuyRight's profit is before the comma, Acme's is after the comma.
a. Describe what is meant by a dominant strategy.
b. Given the payoff matrix above, does each firm have a dominant strategy?
c. Under what circumstances would there be no dominant strategy for one or both firms?

Accepted Answer

The answer of BuyRight is a chain of grocery stores...

Question 20

Use the following statements to answer this question:
I. A player must have at least one dominant strategy in a game.
II. If neither player in a game has a dominant strategy in a game, then there is no equilibrium outcome for the game.
A) I and II are true.
B) I is true and II is false.
C) II is true and I is false.
D) I and II are false.

Accepted Answer

I is false because a player does not necessarily need to have a dominant strategy in a game. A game can be perfectly well-defined and solvable even if no player has a dominant strategy. II is false because the absence of dominant strategies does not imply the absence of an equilibrium outcome. Games without dominant strategies can still have Nash equilibria, where each player's strategy is the best response to the other players' strategies.

Quiz 13: Game Theory and Competitive Strategy

Nash equilibria are stable because

Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs: What are the dominant strategies in this game?

The relationship between a pure-strategy Nash equilibrium and a dominant-strategy equilibrium is that

Scenario 13.5 Consider the following game: -Which of the following is true regarding the game in Scenario 13.5?

A Nash equilibrium occurs when

Use the following statements to answer this question: I. If mixed strategies are allowed, every game has at least one Nash equilibrium. II. The maximin strategy is optimal in the game of "matching pennies."

Scenario 13.6 Consider the following game. Payoffs are in millions of dollars. -In the game in Scenario 13.6,

Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs: What is the Nash equilibrium for this game?

A maximin strategy

Scenario 13.6 Consider the following game. Payoffs are in millions of dollars. -In the game in Scenario 13.6, what is the Nash equilibrium?

Consider the following game in which two firms decide how much of a homogeneous good to produce. The annual profit payoffs for each firm are stated in the cell of the game matrix, and Firm A's payoffs appear first in the payoff pairs: What are the dominant strategies in this game?

In the game in Scenario 13.5,

Scenario 13.4 Consider the following game: -In the game in Scenario 13.4, the equilibrium outcome:

If both players in a game have dominant strategies, we say that the game has:

In a Nash equilibrium,

Scenario 13.6 Consider the following game. Payoffs are in millions of dollars. -Refer to the game in Scenario 13.6. What will occur if ERS Co. plays a maximin strategy?

Use the following statements to answer this question: I. A player must have at least one dominant strategy in a game. II. If neither player in a game has a dominant strategy in a game, then there is no equilibrium outcome for the game.