Deck 14: Game Theory and Strategic Behavior

Question 1

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 3 above,

A)B1 is a dominated strategy for Player B
B)B2 is a dominated strategy for Player B
C)B3 is a dominated strategy for Player B
D)Player B has no dominated strategy.

Answer 1

B

Question 2

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (36-40).
In Game 5 above, in the Nash equilibrium in mixed strategies

A)player B chooses B1 with a 30% probability.
B)player B chooses B1 with a 50% probability.
C)player B chooses B1 with a 60% probability.
D)player B chooses B1 with a 75% probability.

Answer 2

B

Question 3

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 3 above,

A)Player A has a dominant strategy.
B)Player B has a dominant strategy.
C)Both players have a dominant strategy.
D)Neither player has a dominant strategy.

Answer 3

D

Question 4

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (24-25).
In Game 1 above,

A)Player A has a dominant strategy.
B)Player B has a dominant strategy.
C)Both players have dominant strategies.
D)Neither player has a dominant strategy.

Question 5

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (36-40).
In Game 5 above, if the players move sequentially with Player B choosing first, the Nash equilibrium will be

A)Player A choosing A1 and Player B choosing B1.
B)Player A choosing A1 and Player B choosing B2.
C)Player A choosing A2 and Player B choosing B1.
D)Player A choosing A2 and Player B choosing B2.

Question 6

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 4 above,

A)There is one Nash equilibrium.
B)There are two Nash equilibria.
C)There are three Nash equilibria.
D)There are four Nash equilibria.

Question 7

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Suppose in Game 4 above that the players make their choices sequentially, with Player A choosing first. The Nash equilibrium in this game will be,

A)Player A choosing A1 and Player B choosing B1.
B)Player A choosing A1 and Player B choosing B3.
C)Player A choosing A3 and Player B choosing B1.
D)Player A choosing A3 and Player B choosing B3.

Question 8

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 2 above,

A)Player A choosing A1 and Player B choosing B1 is a Nash equilibrium.
B)Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.
C)Player A choosing A2 and Player B choosing B1 is a Nash equilibrium.
D)Player A choosing A2 and Player B choosing B2 is a Nash equilibrium.

Question 9

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 6 above,

A)the Nash equilibrium maximizes the total payoff.
B)the Nash equilibrium does not maximize the total payoff.
C)there is no Nash equilibrium.
D)neither player has a dominant strategy.

Question 10

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 3 above,

A)Player A choosing A1 and Player B choosing B1 is a Nash equilibrium.
B)Player A choosing A1 and Player B choosing B3 is a Nash equilibrium.
C)Player A choosing A3 and Player B choosing B1 is a Nash equilibrium.
D)Player A choosing A3 and Player B choosing B3 is a Nash equilibrium.

Question 11

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
For Game 4 above, which of the following statements is incorrect?

A)Player A choosing A1 and Player B choosing B1 is a Nash equilibrium.
B)Player A choosing A3 and Player B choosing B3 is a Nash equilibrium.
C)Player A choosing A1 and Player B choosing B3 is a Nash equilibrium.
D)Both players in Game 4 have a dominated strategy.

Question 12

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Which statement below is correct concerning Game 2 above?

A)This game is an example of a prisoner's dilemma game.
B)This game is not an example of a prisoner's dilemma game.
C)This game has no Nash equilibrium.
D)This game has multiple Nash equilibria in pure strategies.

Question 13

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (36-40).
In Game 5 above,

A)Player A choosing A1 and Player B choosing B1 is a Nash equilibrium.
B)Player A choosing A2 and Player B choosing B1 is a Nash equilibrium.
C)Player A choosing A1 and Player B choosing B2 is a Nash equilibrium.
D)there are no Nash equilibria in pure strategies.

Question 14

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (36-40).
In Game 5 above,

A)Player A has a dominant strategy.
B)Player B has a dominant strategy.
C)Both players have dominant strategies.
D)Neither player has a dominant strategy.

Question 15

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 6 above,

A)Player A choosing A1 and Player B choosing B1 is a Nash equilibrium.
B)Player A choosing A2 and Player B choosing B2 is a Nash equilibrium.
C)there is no Nash equilibrium.
D)there are multiple Nash equilibria in pure strategies.

Question 16

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (24-25).
In Game 1 above,

A)Player A choosing A1 and Player B choosing B1 is a Nash equilibrium.
B)Player A choosing A2 and Player B choosing B2 is a Nash equilibrium.
C)there is no Nash equilibrium.
D)there are multiple Nash equilibria in pure strategies.

Question 17

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 3 above,

A)A1 is a dominated strategy for Player A
B)A2 is a dominated strategy for Player A
C)A3 is a dominated strategy for Player A
D)Player A has no dominated strategies.

Question 18

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 6 above,

A)Player A has a dominant strategy.
B)Player B has a dominant strategy.
C)both players have dominant strategies.
D)neither player has a dominant strategy.

Question 19

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second (36-40).
In Game 5 above, in the Nash equilibrium in mixed strategies

A)player A chooses A1 with a 2/9 probability.
B)player A chooses A1 with a 3/9 probability.
C)player A chooses A1 with a 4/9 probability.
D)player A chooses A1 with a 5/9 probability.

Question 20

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 2 above,

A)Player A has a dominant strategy.
B)Player B has a dominant strategy.
C)Both players have dominant strategies.
D)Neither player has a dominant strategy.

Question 21

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Game 8 shows the payoff matrix in terms of profit (in millions of dollars)for two possible strategies: advertise or do not advertise. If they legally could, why might the two companies agree to a binding contract committing both to not advertise?

A)Because advertising is ineffective.
B)Because advertising is too expensive.
C)Because not advertising would lower the costs and therefore increase the profits to each firm.
D)Because not advertising would lower profits.

Question 22

Which of the following statements is not true?

A)Nash games cannot have more than one equilibrium.
B)A game can be both Cournot and Nash.
C)A game can be both Bertrand and Nash.
D)Whenever both players have a dominant strategy in a Nash game, that strategy will determine the outcome.

Question 23

Which of the following statements is incorrect?

A)A Nash equilibrium is a situation in which each player chooses their best strategy given the strategies chosen by the other players in the game.
B)A Cournot equilibrium is an example of a Nash equilibrium.
C)A Bertrand equilibrium is an example of a Nash equilibrium.
D)A Nash equilibrium maximizes the aggregate payoffs of the players of the game.

Question 24

Pure strategy:

A)is a specific choice of a strategy from the player's possible strategies in the game, whereas a mixed strategy is a choice between quantity and price optimization.
B)is a specific choice of a strategy outside of the player's possible strategies in the game, whereas a mixed strategy is a choice among two or more pure strategies according to pre-specified probabilities.
C)is a specific choice of a strategy outside of the player's possible strategies in the game, whereas a mixed strategy is a choice between quantity and price optimization.
D)is a specific choice of a strategy from the player's possible strategies in the game, whereas a mixed strategy is a choice among two or more pure strategies according to pre-specified probabilities.

Question 25

Which of the following is most consistent with the concept of a Nash equilibrium?

A)A firm chooses its strategy with regard to pricing in collusion with another firm.
B)A player optimizes his/her outcome in a game by making his/her choice only after the other player has made his/her choice.
C)A firm makes its choice to optimize output without concerning itself as to what other firms are doing.
D)The players always optimize their level of output and no other variable.

Question 26

Reference: In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
In Game 9 above,

A)There is one Nash equilibrium.
B)There are two Nash equilibria.
C)There are three Nash equilibria.
D)There are four Nash equilibria.

Question 27

All of the following statements are true except:

A)In a Nash game, each player will have a dominant strategy.
B)A Cournot equilibrium is an example of a Nash equilibrium.
C)A Bertrand equilibrium is an example of a Nash equilibrium.
D)A game can be both Nash and Cournot at the same time.

Question 28

Game theory refers to:

A)a plan for the actions that a player in a game will take under every conceivable circumstance that the player might face.
B)a situation in which each player chooses the strategy that yields the highest payoff, given the strategy chosen by the other players.
C)optimal decision making by microeconomic agents.
D)the branch of microeconomics concerned with the analysis of optimal decision making in competitive situations.

Question 29

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Game 8 shows the payoff matrix in terms of profit (in millions of dollars)for two possible strategies: advertise or do not advertise. Which of the following is a true statement?

A)Coke has a dominant strategy to not advertise.
B)Pepsi has a dominant strategy to not advertise.
C)The game has one Nash equilibrium.
D)The game has multiple equilibria.

Question 30

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Game 7 is an example of prisoners' dilemma. Thus, the payoff matrix contains jail sentences in terms of months. For this game,

A)the Nash equilibrium minimizes the total number of months spent in jail for both prisoners.
B)the Nash equilibrium does not minimize the total number of months spent in jail for both prisoners.
C)there is no Nash equilibrium.
D)neither player has a dominant strategy.

Question 31

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Game 8 shows the payoff matrix in terms of profit (in millions of dollars)for two possible strategies: advertise or do not advertise. Suppose that the two companies can legally make a non-binding agreement to not advertise. Based on the payoff matrix shown above, will the two companies honor such an agreement to not advertise?

A)Yes. Both Coke and Pepsi will not advertise.
B)No. Coke will advertise but Pepsi will not.
C)No. Pepsi will advertise but Coke will not.
D)No. Both Coke and Pepsi will advertise.

Question 32

Reference: In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Game 9 has the structure of a

A)prisoner's dilemma.
B)sequential game.
C)game of chicken.
D)tit-for-tat game

Question 33

A dominant strategy:

A)is a strong strategy.
B)guarantees a Nash equilibrium.
C)is a strategy that is better for a player than any other the player might choose, regardless of the other player's strategy.
D)depends on the other player's strategy.

Question 34

In a simultaneous move game with two players,

A)if neither player has a dominant strategy, we successively eliminate each player's subordinate strategy.
B)a player chooses among two or more pure strategies according to pre-specified probabilities.
C)if one player has a dominant strategy and the other doesn't, you can't reach a Nash equilibrium.
D)if both players have a dominant strategy, these constitute their Nash equilibrium strategies.

Question 35

Reference: In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Games with structures like Game 9 above have been used to describe:

A)bank runs.
B)collusion in Sumo wrestling.
C)dominant strategy equilibria.
D)the decision to hire a lawyer.

Question 36

Under a mixed strategy,

A)players move sequentially.
B)a player chooses among two or more pure strategies according to pre-specified probabilities.
C)the players may never reach a Nash equilibrium.
D)players obtain lower payoffs than in a pure strategy equilibrium.

Question 37

In the following games, all payoffs are listed with the row player's payoffs first and the column player's payoffs second.
Game 7 is an example of prisoners' dilemma. Thus, the payoff matrix contains jail sentences in terms of months. For this game,

A)Player A has a dominant strategy.
B)Player B has a dominant strategy.
C)both players have dominant strategies.
D)neither player has a dominant strategy.

Question 38

Player A has a dominated strategy:

A)when Player A has a dominant strategy.
B)in a game of chicken
C)when Player A has another strategy that gives a higher payoff regardless of what Player B does.
D)when there are less than three players per game.

Question 39

The prisoners' dilemma shows that in a Nash equilibrium:

A)neither player can have a better result than the other.
B)sometimes players do not reach the optimal outcome.
C)only an irrational strategy will lead to an outcome worse than the optimal outcome.
D)each player acting independently will lead to the optimal outcome.

Question 40

A prisoners' dilemma game illustrates the conflict between:

A)law enforcement and criminals.
B)the judicial system and the police system.
C)law and order.
D)self-interest and collective interests.

Question 41

The likelihood of a cooperative outcome in a repeated prisoners' dilemma type game decreases when:

A)they value payoffs in future periods much less than they value payoffs in the current period.
B)interactions between the players are frequent.
C)cheating is easy to detect.
D)the one-time gain from cheating is small in comparison to the eventual cost of cheating.

Question 42

A game tree is:

A)a diagram that shows the different strategies that each player can follow in a game and the viability of those strategies for each player.
B)a diagram that shows the different strategies that each player can follow in a game and the probability that each player will choose each strategy.
C)a diagram that shows the different strategies that each player can follow in a game and the order in which those strategies get chosen.
D)a diagram that shows the optimal strategy for each player.

Question 43

Nash games cannot have more than one equilibrium.

Question 44

Consider a repeated prisoner's dilemma game. The likelihood of a cooperative outcome rises when:

A)they value payoffs in future periods much less than they value payoffs in the current period.
B)Interactions between the players are frequent.
C)Cheating is difficult to detect.
D)The one-time gain from cheating is large in comparison to the eventual cost of cheating.

Question 45

A game situation in which there is a tension between the collective interest of all of the players and the self-interest of individual players is called a "prisoner's dilemma".

Question 46

A strategy in which you do to your opponent in this period what your opponent did to you in the last period is a:

A)live-and-let-live strategy
B)shoot-to-kill strategy.
C)grim trigger strategy.
D)tit-for-tat strategy.

Question 47

Backward induction refers to:

A)a procedure for solving a sequential-move game by starting at the beginning of the game tree and finding the optimal decision for the player at each decision point.
B)a procedure for solving a sequential-move game by starting at the end of the game tree and finding the best response function at each decision point.
C)a procedure for solving a sequential-move game by starting at the end of the game tree and finding the player's motives for making the decision at each decision point.
D)a procedure for solving a sequential-move game by starting at the end of the game tree and finding the optimal decision for the player at each decision point.

Question 48

A game can be both Cournot and Nash.

Question 49

In a Nash game, each player will have a dominant strategy.

Question 50

A Cournot equilibrium is an example of a Nash equilibrium.

Question 51

Player A and Player B are playing a prisoners' dilemma game. Which of the following statements is false?

A)If the players play the game repeatedly with each other, the players may play cooperatively.
B)If the game is played only once, the players would not be expected to cooperate.
C)If players play the game repeatedly with each other, they are more likely to cooperate if they are patient.
D)If the game is played only once, the outcome minimizes total jail time.

Question 52

Whenever both players have a dominant strategy in a Nash game, that strategy will determine the outcome.

Question 53

The Cournot and Bertrand models are examples of "prisoner's dilemma" games.

Question 54

In a sequential game:

A)A player always obtains a higher payoff by maintaining the maximum flexibility in his or her actions.
B)The first mover always obtains a higher payoff than a second mover.
C)A player can sometimes obtain a higher payoff by making a move that restricts the flexibility he or she will have later in the game.
D)strategic moves include those that are easy to reverse.

Question 55

In order to solve a sequential game:

A)The game is generally solved from the end of the game tree, finding the optimal decision at each decision point and working back to the beginning.
B)The game is generally solved from the beginning of the game tree, finding the optimal decision at each decision point and working towards the end.
C)Only a single player's payoffs are necessary.
D)Tit-for-tat strategies are particularly helpful.

Question 56

A game can be both Nash and Cournot at the same time.

Question 57

A Nash equilibrium is a situation in which each player chooses their best strategy given the strategies chosen by the other players in the game.

Question 58

The likelihood of a cooperative outcome in a repeated prisoners' dilemma type game increases when:

A)interactions between the players are frequent.
B)the players are impatient.
C)cheating is not detectable.
D)there is a large gain from cheating.

Question 59

A game can be both Bertrand and Nash.

Question 60

A Bertrand equilibrium is an example of a Nash equilibrium.

Question 61

A Bertrand equilibrium is an example of a Nash equilibrium.

Question 62

A Cournot equilibrium is an example of a Nash equilibrium.

Question 63

A Nash equilibrium maximizes the aggregate payoffs of the players of the game.

Question 64

Player A and Player B are playing a prisoners' dilemma game. If the players play the game repeatedly with each other, the players may play cooperatively.

Question 65

Player A and Player B are playing a prisoners' dilemma game. If the game is played only once, the outcome minimizes total jail time.

Question 66

Player A and Player B are playing a prisoners' dilemma game. If the game is played only once, the players would not be expected to cooperate.

Question 67

Player A and Player B are playing a prisoners' dilemma game. If players play the game repeatedly with each other, they are more likely to cooperate if they are patient.

Question 68

The concept of backwards induction applies to both simultaneous and sequential games.

Question 69

A simultaneous game is commonly represented in a game matrix, whereas a sequential game is commonly represented with a game tree.