Deck 12: The Theory of Games

Question 1

An outcome that is Pareto optimal is preferred by both players to all other possible outcomes.

Answer 1

False

Question 2

The main problem in the Prisoners' Dilemma is that the players involved fail to agree on an outcome that would be mutually beneficial.

Answer 2

True

Question 3

It is always best to be the strong pig in Pigs in a Box.

Answer 3

False

Question 4

An outcome is not a Nash equilibrium if either player would be better off with a different strategy.

Question 5

A solution concept is any way of analyzing a game which leads to the discovery of a Nash equilibrium which solves the game.

Question 6

If either player is receiving his maximum payoff,then that outcome is Pareto optimal.

Question 7

The copycat game does not have a pure strategy Nash Equilibrium.

Question 8

In any game situation,at least one player always has a dominant strategy.

Question 9

When mixed strategies are allowed,the Copycat Game does have a Nash equilibrium.

Question 10

A player has a dominant strategy when there is one strategy the player would want to follow regardless of the other player's behavior.

Question 11

The concept of Nash Equilibrium is an important solution concept because it helps make predictions.

Question 12

When both players have dominant strategies,there is one and only one Nash equilibrium.

Question 13

The Battle of the Sexes game has two Nash equilibria,neither of which is Pareto optimal.

Question 14

Nash equilibrium is a normative concept.

Question 15

An outcome is a Nash equilibrium if and only if both players agree that the outcome is desirable.

Question 16

When a game has more than one Nash equilibrium,it is unlikely that a stable equilibrium will ever be reached.

Question 17

For a Nash equilibrium to exist,at least one player must have a dominant strategy.

Question 18

When both players have dominant strategies,there is only one Nash equilibrium.

Question 19

All outcomes in the Copycat Game are Nash equilibria.

Question 20

For an outcome to be Pareto optimal,the players' total payoff must be as large as possible.

Question 21

When a game has more than one Nash equilibrium,

A) at least one of them will be Pareto optimal.
B) they will all tend to be unstable.
C) they must provide the same total payoff to the players.
D) it is difficult to predict which of them will actually occur.

Question 22

In the Prisoners' Dilemma game,the only outcome that is not Pareto optimal is also the game's only Nash equilibrium.

Question 23

A system for studying strategic behavior in economics is called

A) decision science.
B) political economy.
C) game theory.
D) solution concepts.

Question 24

In the Battle of the Sexes game,

A) Fred and Ethel are best off choosing the activity they prefer.
B) Fred is better off attending the opera with Ethel than having Ethel attend the boxing match with him.
C) Ethel is better off attending the boxing match with Fred than having Fred attend the opera with her.
D) Fred and Ethel would both be better off choosing to attend either activity together than going alone to the activity they prefer.

Question 25

Consider a two-person,two-strategy game in which only pure strategies are played.Such a game must have at least one

A) Nash equilibrium.
B) player with a dominant strategy.
C) Pareto-optimal outcome.
D) outcome that is both a Nash equilibrium and Pareto optimal.

Question 26

When neither player in a game would want to deviate from a particular outcome,taking the opponent's behavior as given,the outcome is

A) a Stackelberg equilibrium.
B) Pareto optimal.
C) a Nash equilibrium.
D) a dominant strategy.

Question 27

In any game,all that is necessary to rule out an outcome is that

A) both players would want to change.
B) one player would want to change.
C) one player is worse off than with some other strategy.
D) both players are worse off than with some other strategy.

Question 28

The Stackelberg equilibrium of a sequential game must also be a Nash equilibrium.

Question 29

A dominant strategy is one which

A) is best for a player no matter what strategy the other player chooses.
B) is optimal given the other player's strategy,but may not be optimal should the other player switch strategies.
C) will lead to a Pareto-optimal outcome.
D) will be chosen by the first player in a sequential game.

Question 30

In the Prisoners' Dilemma game,

A) the Nash equilibrium is the only outcome that is not Pareto optimal.
B) neither player has a dominant strategy.
C) the Stackelberg equilibrium will be Pareto optimal if the game is played sequentially.
D) all possible outcomes are Nash equilibria.

Question 31

Consider the Prisoners' Dilemma game,and suppose one player confesses but the other player does not confess.This outcome is

A) a Nash equilibrium.
B) Pareto optimal.
C) a Pareto improvement over the outcome where both players confess.
D) Pareto-inferior to the outcome where neither player confesses.

Question 32

A Cournot equilibrium arises when one player announces his strategy before the other.

Question 33

A game's outcome is a Nash equilibrium when

A) any attempt to improve one player's payoff will lower the other player's payoff.
B) neither player wants to change his strategy,given the strategy chosen by the other player.
C) the total payoff to the players is as large as possible.
D) the first player has selected his strategy taking the second player's optimal response into account.

Question 34

When both players in a game play a dominant strategy,the outcome will be

A) Pareto optimal.
B) a Prisoners' Dilemma.
C) a Stackelberg equilibrium.
D) the game's only Nash equilibrium.

Question 35

When a game is played sequentially,the first player will have an advantage over the second player.

Question 36

In the Battle of the Sexes game,there

A) are two Nash equilibria,neither of which is Pareto optimal.
B) is one Nash equilibrium and it is not Pareto optimal.
C) is one Nash equilibrium and it is Pareto optimal.
D) are two Nash equilibria,both of which are Pareto optimal.

Question 37

Consider an outcome in which it is impossible to make one player better off without simultaneously making the other player worse off.We can conclude that this outcome

A) cannot be a Nash equilibrium.
B) must be Pareto optimal.
C) will not occur when the players use mixed strategies.
D) is a Stackelberg equilibrium.

Question 38

A Nash equilibrium need not be Pareto optimal,and a Pareto-optimal outcome need not be a Nash equilibrium.

Question 39

The diagram used to show one player's strategies across the top and the other player's strategies along the left,with the corresponding outcomes in the appropriate boxes is a

A) game matrix.
B) flow chart.
C) mixed strategy.
D) an oligopoly problem.

Question 40

In a sequential game,guaranteed commitment to a strategy will make a player worse off.

Question 41

It is unlikely that players will attain the Stackelberg equilibrium if

A) both players have a dominant strategy.
B) the Stackelberg equilibrium is Pareto preferred to the Nash equilibrium.
C) the second player cannot be assured that the first player is committed to his strategy.
D) there is an advantage to being the second player.

Question 42

Game Matrix III

The following questions refer to the game matrix below. Each firm has a choice of advertising, Ads, or not advertising, No ad. The profits each gets depend upon which it chooses.



-Refer to Game Matrix III.The Nash equilibrium is to be found where

A) neither firm advertises.
B) Firm A advertises,Firm B does not.
C) Firm A does not advertise but Firm B does.
D) both firms choose to advertise.

Question 43

Game Matrix I

The following questions refer to the game matrix below.



-Refer to Game Matrix I.If this game is played sequentially with Player A choosing first,the Stackelberg equilibrium is

A) the upper left-hand corner.
B) the upper right-hand corner.
C) the lower left-hand corner.
D) the lower right-hand corner.

Question 44

Which of the following is a normative concept?

A) Nash equilibrium.
B) Stackelberg equilibrium.
C) Pareto optimality.
D) Nash equilibrium,Stackelberg equilibrium,and Pareto optimality are all normative concepts.

Question 45

Game Matrix II
The following questions refer to the game matrix below. Player A can play the strategies "High" and "Low," and Player B can play the strategies "Odd" and "Even."


-Refer to Game Matrix II.Which outcomes in this game are Pareto optimal?

A) The upper right-hand corner only.
B) The lower right-hand corner only.
C) Both the upper and lower right-hand corners.
D) All outcomes except the upper left-hand corner.

Question 46

Game Matrix I

The following questions refer to the game matrix below.



-Refer to Game Matrix I.The only outcome in this game that is not Pareto optimal is

A) the upper left-hand corner.
B) the upper right-hand corner.
C) the lower left-hand corner.
D) the lower right-hand corner.

Question 47

Game Matrix II
The following questions refer to the game matrix below. Player A can play the strategies "High" and "Low," and Player B can play the strategies "Odd" and "Even."


-Refer to Game Matrix II.Assume this game is played sequentially.When is the Stackelberg equilibrium of this game also Pareto optimal?

A) Always.
B) When A is the first player.
C) When B is the first player.
D) Never.

Question 48

Game Matrix II
The following questions refer to the game matrix below. Player A can play the strategies "High" and "Low," and Player B can play the strategies "Odd" and "Even."


-Refer to Game Matrix II.Which outcomes in this game are Nash equilibria?

A) The upper right-hand corner only.
B) The upper left-hand corner only.
C) Both the upper right-hand and lower left-hand corners.
D) This game has no Nash equilibria.

Question 49

When a player randomly chooses the strategy to play,with each strategy given a fixed probability of being chosen,we say that the player is using

A) a mixed strategy.
B) a pure strategy.
C) a dominant strategy.
D) a Stackelberg strategy.

Question 50

Game Matrix III

The following questions refer to the game matrix below. Each firm has a choice of advertising, Ads, or not advertising, No ad. The profits each gets depend upon which it chooses.



-Refer to Game Matrix III.In this game,

A) Firm A's dominant strategy is to advertise.
B) Firm A's dominant strategy is not to advertise.
C) Firm B's dominant strategy is to advertise.
D) Firm B has no dominant strategy.

Question 51

Suppose that,in a sequential game,the first player chooses the strategy with the highest payoff,taking into account an optimal response from the second player.The outcome that results is

A) a Nash equilibrium.
B) Pareto optimal.
C) a Prisoners' Dilemma.
D) a Stackelberg equilibrium.

Question 52

In the copycat game,there

A) is one Nash equilibrium.
B) are two Nash equilibria.
C) all the outcomes are Nash equilibria.
D) no matter what Ditto chooses,Dot would prefer the other activity.

Question 53

A solution concept for a game is

A) a measurement of the game's complexity.
B) a way of determining whether the first or second player has an advantage.
C) a normative judgment of the desirability of the game's outcome.
D) a rule for predicting the game's outcome when it is actually played.

Question 54

Game Matrix II
The following questions refer to the game matrix below. Player A can play the strategies "High" and "Low," and Player B can play the strategies "Odd" and "Even."


-Refer to Game Matrix II.When would the upper left-hand corner be the likely outcome of this game?

A) When the game is played sequentially,with A being the first player.
B) When the game is played sequentially,with B being the first player.
C) When the players choose their strategies simultaneously.
D) The upper left-hand corner would never be the likely outcome,because the upper right-hand corner makes both player better off.

Question 55

Game Matrix II
The following questions refer to the game matrix below. Player A can play the strategies "High" and "Low," and Player B can play the strategies "Odd" and "Even."


-Refer to Game Matrix II.In this game,

A) players A and B both have dominant strategies.
B) player A has a dominant strategy,but player B does not.
C) player B has a dominant strategy,but player A does not.
D) neither player has a dominant strategy.

Question 56

Game Matrix I

The following questions refer to the game matrix below.



-Refer to Game Matrix I.The only Nash equilibrium for this game is in

A) the upper left-hand corner.
B) the upper right-hand corner.
C) the lower left-hand corner.
D) the lower right-hand corner.

Question 57

If mixed strategies are allowed in the Copycat Game,a Nash equilibrium will result if

A) both players randomly choose their strategies by flipping a fair coin.
B) one player randomly chooses his strategy by flipping a fair coin,while the other player uses a pure strategy.
C) one player randomly chooses his strategy by flipping an unfair coin,while the other player uses a pure strategy.
D) both players stick to using pure strategies.

Question 58

When a game has more than one Nash equilibrium

A) players will choose the strategies which maximize total welfare.
B) players are likely to choose the strategies which minimize total welfare.
C) it is difficult to predict which of the equilibria will occur or whether it is stable.
D) it is difficult to predict which of the equilibria will occur but once one is reached it is likely to remain stable.

Question 59

Since Ditto can always be expected to choose the same activity as Dot in the copycat game

A) any move by Dot to escape from Ditto would not be a Pareto improvement.
B) any move by Dot to escape from Ditto would be a Pareto improvement.
C) Ditto's choice to follow Dot is a Pareto improvement over going by himself.
D) Ditto's choice to follow Dot would be a Pareto improvement over playing by himself so long as Dot does not move.

Question 60

Game Matrix I

The following questions refer to the game matrix below.



-Refer to Game Matrix I.What are the dominant strategies in this game?

A) A's dominant strategy is ,and B's dominant strategy is https://d2lvgg3v3hfg70.cloudfront.net/TB7494/.
B) A's dominant strategy is 11ef8b91_15e3_4858_85d9_ed30eda92b82_TB7494_11,but B does not have a dominant strategy.
C) B's dominant strategy is 11ef8b91_30d8_fc49_85d9_e349c126c0c6_TB7494_11,but A does not have a dominant strategy.
D) Neither player has a dominant strategy.

Question 61

Game Matrix III

The following questions refer to the game matrix below. Each firm has a choice of advertising, Ads, or not advertising, No ad. The profits each gets depend upon which it chooses.



-Refer to Game Matrix III.Which of the following is a property of this game?

A) Both firms have dominant strategies.
B) There is no pure strategy Nash equilibrium.
C) There is a Nash equilibrium and it is Pareto optimal.
D) There is a Nash equilibrium and it is not Pareto optimal.

Question 62

Consider a game in which a player has a dominant strategy.

Question 63

Fuji and Kodak produce identical film.The market demand for film is given by P = 8 - Q,where P is the price (in dollars per roll of film)and Q is the quantity (in hundreds of rolls).Each firm has the option of producing 150,200,or 300 rolls of film at a constant marginal cost of $2 per roll with no fixed costs.The firms' possible profits for various outcomes are summarized in the accompanying table.

Question 64

Game Matrix V

The following questions refer to the game matrix below. Each firm has a choice of saying Yes or NO. The profits each gets depend upon which it chooses.



-Refer to Game Matrix V.Which of the following values of X and Y result in there being no pure strategy Nash Equilibrium?

A) X = 21,Y = 9.
B) X = 19,Y = 11.
C) X = 31,Y = 11.
D) There will always be at least one pure strategy Nash Equilibrium in this game.

Question 65

Consider a game in which all outcomes give the players the same total payoff.Explain why every outcome in such a game will be Pareto optimal.

Question 66

Game Matrix IV

The following questions refer to the game matrix below.

Player A can play the strategies UP and DOWN and Player B can play the strategies LEFT and RIGHT.



-Refer to Game Matrix IV.The Nash Equilibrium for the game is

A) UP,LEFT
B) UP,RIGHT
C) DOWN,LEFT
D) DOWN,RIGHT

Question 67

Define the term Nash equilibrium.In general,what can be claimed about the existence,uniqueness,and Pareto optimality of Nash equilibria? Support your answers with appropriate examples.

Question 68

Which of the following statements is false?

A) Player A has a dominant strategy.
B) Player B has a dominant strategy.
C) This is a Prisoners' Dilemma.
D) This game has no Nash Equilibrium.

Question 69

Game Matrix V

The following questions refer to the game matrix below. Each firm has a choice of saying Yes or NO. The profits each gets depend upon which it chooses.



-Refer to Game Matrix V.If X = 15 and Y = 15,then

A) Player A has a dominant strategy,but Player B does not.
B) Player B has a dominant strategy,but Player A does not.
C) Both Players A and B have dominant strategies.
D) Neither Players have dominant strategies.

Question 70

What is a mixed strategy? Describe a mixed strategy that would be a Nash equilibrium for the Copycat Game,and indicate why neither player would want to deviate from that mixed strategy.

Question 71

Game Matrix V

The following questions refer to the game matrix below. Each firm has a choice of saying Yes or NO. The profits each gets depend upon which it chooses.



-Refer to Game Matrix V.Which of the following values of X and Y result in the only Nash Equilibrium being (No,No)and there also being a Prisoners' Dilemma?

A) X = 21,Y = 9.
B) X = 19,Y = 11.
C) X = 31,Y = 11.
D) It is not possible for (No,No)to be a Nash Equilibrium and for there to be a Prisoners' Dilemma.

Question 72

Consider each pair of strategies other than UP,RIGHT.Which of the following statements is not true about those pairs?

A) They are all Pareto Optimal.
B) None of them are a Nash Equilibrium.
C) The players would not mutually agree to play any of them if such an agreement were possible.
D) Each requires that a player play a dominate strategy.

Question 73

Game Matrix V

The following questions refer to the game matrix below. Each firm has a choice of saying Yes or NO. The profits each gets depend upon which it chooses.



-Refer to Game Matrix V.Which of the following values of X and Y result in the only Nash Equilibrium being (No,No)and there not being a Prisoners' Dilemma?

A) X = 21,Y = 9.
B) X = 19,Y = 11
C) X = 31,Y = 11.
D) It is not possible for (No,No)to be a Nash Equilibrium and for there not to be a Prisoners' Dilemma.

Question 74

One reason that DOWN,RIGHT is not a NASH equilibrium is that

A) Player B receives a payoff of 8 as opposed to the payoff of 20 that he would receive if he changed his strategy.
B) Player B receives a payoff of 20 as opposed to the payoff of 30 that he would receive if he changed his strategy.
C) Player A receives a payoff of 20 as opposed to the payoff of 30 that he would receive if he changed his strategy.
D) DOWN,RIGHT is a Nash equilibrium.

Question 75

Can a Nash equilibrium fail to be Pareto optimal? Can a Pareto optimal outcome fail to be a Nash equilibrium? Justify your answers using the Prisoners' Dilemma game.

Question 76

Game Matrix V

The following questions refer to the game matrix below. Each firm has a choice of saying Yes or NO. The profits each gets depend upon which it chooses.



-Refer to Game Matrix V.Which of the following values of X and Y result in the only Nash Equilibrium being (Yes,Yes)?

A) X = 21,Y = 9.
B) X = 19,Y = 11.
C) X = 21,Y = 11.
D) It is not possible for (Yes,Yes)to be a Nash Equilibrium.

Question 77

Consider the simultaneous choice game represented by the matrix below where Player A chooses either Up or Down and Player B chooses either Left or Right.