Question 1

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 chosen strategy, given the strategy of the other player. In this game, player 1's best response to player 2 playing Defect is to also play Defect, as they will earn $2 million instead of $1 million. Similarly, player 2's best response to player 1 playing Defect is to also play Defect, as they will earn -$0.5 million instead of -$1 million. Therefore, (Defect, Defect) is the Nash equilibrium strategy pair.

Question 2

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 3

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 4

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 maximizes the minimum gain that can be earned, which is typically a safer and more conservative approach. This ensures that even in the worst-case scenario, the player still walks away with a decent gain.

Question 5

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, assuming the other firms' strategies remain unchanged.

Question 6

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 7

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. The players choose their strategies based on what they believe others will do and try to maximize their own payoffs. Each player's strategy is a best response to the strategies chosen by the other players. Therefore, there may not be a single dominant strategy for any player, leading to a situation where no player can benefit by changing their strategy.

Question 8

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

A Nash equilibrium is stable because no player can benefit by changing their strategy unilaterally, given the strategies of the other players.

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

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 11

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

In order for the dam to be built the citizens must contribute a total of $1,000,000 ($1,000 x 1,000 citizens). If every citizen contributes, the dam is built and each citizen receives $70,000, resulting in a total payoff of $69,000 for each citizen after their initial contribution of $1,000.

If a player chooses not to contribute, the dam will not be built and they will receive a payoff of $0. However, if all players choose not to contribute, the town will suffer from flooding and each player will receive a payoff of - $10,000 (representing the damages incurred by each person).

Therefore, the strategy pair that pays $69,000 to each player (if all players contribute) and the strategy pair that pays $0 to each player (if no player contributes) are equilibria. Thus, the correct answer is E.

Question 12

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 there exists a set of strategies for both players where each player's best response is always the same regardless of what the other player does. This is known as the equilibrium in dominant strategies, making option D the correct answer. Option A is incorrect as it refers to a different concept known as constant sum games. Option B and C are also incorrect as they are not relevant to the scenario described in the question.

Question 13

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 14

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 15

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 as he is choosing to use different strategies (backhand, forehand, and straight) with a certain probability (20%, 30%, and 50%). A pure strategy would involve choosing only one specific strategy (such as serving only to Federer's backhand). A dominant strategy would be a strategy that would always be the best choice, regardless of what the opponent does, but Agassi's choices will depend on Federer's reactions. A maximin strategy involves choosing the best possible option based on the worst possible outcome, but Agassi's choices again will depend on Federer's reactions. Therefore, the best choice for Agassi is a mixed strategy.

Question 16

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 17

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.

Question 18

Scenario 13.5
Consider the following game: 
-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 in the West, as it yields a higher payoff regardless of the other player's choice. However, if both players choose to expand in the West, they will end up with a lower payoff compared to if one player expands in the South and the other player expands in the West. Therefore, the equilibrium is for one player to choose to expand in the West and the other player to expand in the South. This results in two equilibria, one where Player A expands West and Player B expands South, and the other where Player B expands West and Player A expands South.

Question 19

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 20

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 situation in which each player's optimal strategy is independent of the strategies chosen by other players. A pure-strategy Nash equilibrium is a situation in which each player's strategy is a best response to the strategies chosen by the other players. Therefore, a dominant-strategy equilibrium is a special case of a pure-strategy Nash equilibrium, where each player's dominant strategy happens to be their best response to the other players. However, not all pure-strategy Nash equilibria are dominant-strategy equilibria, since there may be cases where a player has multiple best responses, but only one dominant strategy.

Quiz 13: Game Theory and Competitive 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?

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

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 maximin strategy:

A Nash equilibrium occurs when:

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?

In a Nash equilibrium,

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 is the Nash equilibrium for this game?

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

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

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

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?

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.

Scenario 13.5 Consider the following game: -In the game in Scenario 13.5,

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: