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1. Which of the following conditions, if present, is sufficient to make a game cooperative?

a. Individual payoffs are greater if all players choose the same strategy.

b. Players can communicate with each other.

c. Players can negotiate binding contracts committing them to particular strategies.

d. Players must agree unanimously on any set of strategies.

e. The payoff that is highest for all individuals together is also highest for each individual player.

2. You are playing a game in which a dollar bill is auctioned. The highest bidder receives the dollar in return for the amount bid. However, the second-highest bidder must pay the amount that he or she bids, and gets nothing in return. The optimal strategy is:

a. to bid the smallest allowable increment below $1.

b. to bid nothing.

c. to bid $0.99.

d. to bid more than a dollar.

3. Which of the following are examples of cooperative games?

a. the bargaining between a buyer and seller over the price of a car

b. independent action by two firms in a market regarding advertising strategies

c. independent pricing strategies by two firms in a market

d. independent pricing strategies by many firms in a market

e. team games (such as baseball or basketball).

4. In Spring 1994, Northwest Airlines took the independent action of reducing fares on its flights. Other competing airlines quickly matched the fare cuts. These actions might be interpreted as:

a. a noncooperative game.

b. a cooperative game.

c. a constant sum game.

d. a competitive game.

Use the following information to answer the questions below:

You are negotiating with your florist over the price of flowers

for your wedding. You value the floral arrangements at $500. It

cost your florist $200 to do the arrangements. You finally

settled on a price of $250.

5. Your negotiations are an example of:

a. a noncooperative game.

b. a cooperative game.

c. a constant sum game.

d. a competitive game.

e. both (b) and (c)

6. At your negotiated price your consumer surplus is: a. $0

a. $50

b. $200

c. $250

d. $300

 

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7. At your negotiated price the producer surplus is:

a. $0

b. $50

c. $200

d. $250

e. $300

8. If your negotiated price had been $350 instead of $250, the sum of consumer surplus and producer surplus would be:

a. less than what would have accrued at the $250 price.

b. the same as what would have accrued at the $250 price.

c. more than what would have accrued at the $250 price.

d. none of the above is necessarily correct.

9. A dominant strategy can best be described as

a. a strategy taken by a dominant firm.

b. the strategy taken by a firm in order to dominate its rivals.

c. a strategy that is optimal for a player no matter what an opponent does.

d. a strategy that leaves every player in a game better off.

e. all of the above.

10. Your economics professor has decided that your class will not be graded on a curve but on an absolute scale. Therefore, it is possible for every student in the class to get an "A." Your grade will not depend in anyway on your classmates performance. Based on this information, you decide that you should study economics three hours each day, regardless of what your classmates do. In the language of game theory, your decision to study three hours each day is:

a. a dominant strategy.

b. a minimax strategy.

c. a maximin strategy.

d. a prisoners' dilemma.

11. A strategy A is "dominant" for a player X if

a. strategy A contains among its outcomes the highest possible payoff in the game.

b. irrespective of any of the possible strategies chosen by the other players, strategy A generates a higher payoff than any other strategy available to player X.

c. strategy A is the best response to every strategy of the other player.

d. strategy A is the best response to the best strategy of the other player.

e. every outcome under strategy A generates positive payoffs.

 

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For the questions below, consider the following game:

ABC Inc.

컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴

Offer Rebate No Rebate

旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커

XYZ Corp Offer Rebate 20, 10 30, 0

No Rebate 12, 16 20, 4

읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸

12. Which of the following is true about the above game?

a. ABC's dominant strategy is to offer a rebate.

b. ABC's dominant strategy is not offer no rebate.

c. XYZ's dominant strategy is to offer a rebate.

d. XYZ's dominant strategy is not offer no rebate.

e. Both ABC and XYZ have rebate as a dominant strategy.

13. In the above game, the equilibrium strategies

a. are for both firms to offer rebates.

b. is for ABC to offer a rebate, and XYZ not to.

c. is for XYZ to offer a rebate, and ABC not to.

d. are for both firms to offer no rebate.

e. does not exist in pure strategies.

For the questions below, consider the following game:

Zport Co.

컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴

Offer LoProfile Offer

Tires Sunroof

旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커

Moto Corp. Offer CD Changer 40, 400 100, 200

Offer Free

Maintenance 0, 300 160, 120

읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸

14. Which of the following is true for the above game?

a. Moto's dominant strategy is the CD changer.

b. Moto's dominant strategy is the free maintenance.

c. Zport's dominant strategy is the low-profile tires.

d. Zport's dominant strategy is the sunroof.

e. Neither company has a dominant strategy.

15. In the above game, equilibrium

a. is for Moto to offer a CD changer and Zport to offer low-profile tires.

b. is for Moto to offer a CD changer and Zport to offer a sunroof.

c. is for Moto to offer free maintenance and Zport to offer low-profile tires.

d. is for Moto to offer free maintenance and Zport to offer a sunroof.

e. does not exist in pure strategies.

 

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For the questions below, consider the following game:

Vita Bars

컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴

Sponsor Sponsor TV

Marathon Running Show

旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커

NRG Bars Sponsor Marathon 5, 9 9, 6

Sponsor TV

Running Show 8, 14 3, 16

읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸

16. Which of the following is true for the above game?

a. NRG's dominant strategy is to sponsor the marathon.

b. NRG's dominant strategy is to sponsor the TV show.

c. Vita's dominant strategy is to sponsor the marathon.

d. Vita's dominant strategy is to sponsor the TV show.

e. Neither company has a dominant strategy.

17. In the above game, equilibrium

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.

For the questions below, consider the following game:

Bull Meat

컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴

Expand in the Expand in the

West South

旼컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴커

Deer Meat Expand in the 10, 60 50, 90

West

Expand in the

South 20, 80 40, 50

읕컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴켸

18. Which of the following is true?

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.

19. In the game above,

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.

 

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20. 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.

21. 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.

22. Andre Agassi, a star tennis player, is playing the number one player in the world, Pete Sampras. Before the match, Agassi decided that he would serve 20 percent of his serves to Sampras' backhand, 30 percent of his serves to Sampras' forehand, and 50 percent of his serves straight at Sampras. 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.

23. 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.

24. 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.

25. 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.

 

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

a. dominant-strategy equilibrium is a special case of pure-strategy Nash equilibrium.

b. pure-strategy Nash equilibrium is a special case of 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.

For the questions below, consider the following game. Payoffs are in millions of dollars.

Lawrence LLP

27. In the above game,

a. "Poison Pill" is a dominant strategy for Lawrence LLP.

b. "Dump" is a dominant stratetgy 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.

28. In the above game, what is the Nash equilibrium?

a. The strategy pair associated with -$100, -$1.

b. The strategy pair associated with $2, -$.5.

c. The strategy pair associated with $1, -$1.

d. The strategy pair associated with -$.5, -$.5.

e. There is no Nash equilibrium in pure strategies.

29. What will occur if ERS Co. plays a maximin strategy?

a. -$100, -$1

b. $2, -$.5

c. $1, -$1

d. -$.5, -$.5

e. There is a .25 chance of each outcome in that case.

 

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For the following questions, 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 $1000 to the dam in order for it to be built. The dam, if built, is worth $70,000 to each citizen.

One Citizen

30. In the above game, 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.

31. If each player chose a maximin strategy the outcome would be

a. $69,000, $69,000.

b. $0, -$1000.

c. -$1000, $0.

d. $0, $0.

e. a mixed strategy equilibrium.

For the following questions, consider the game below.

IVY Corp

32. The above game is

a. variable-sum.

b. constant-sum.

c. cooperative.

d. a Prisoners' Dilemma.

e. a Conjoint Crux.

 

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33. In the above game,

a. Y is a dominant strategy for IVY Corp.

b. Z is a dominant strategy for IVY Corp.

c. A is a dominant strategy for SAC Group.

d. B is a dominant strategy for SAC Group.

e. No firm has a dominant strategy.

34. In the above game, what is the Nash equilibrium?

a. The strategy pair associated with $1, $10.

b. The strategy pair associated with $2, $0.

c. The strategy pair associated with $1, -$5000.

d. The strategy pair associated with $2, $2.

e. There is no Nash equilibrium in pure strategies.

35. In the above game, what will occur if IVC Corp. plays a maximin strategy?

a. $1, $10

b. $1, -$5000

c. $2, $0

d. $2, $2

e. There is a .25 chance of each outcome in that case.

For the following questions, consider the game below.

It costs each lakeside firm $1500 per period to use filters

that avoid polluting the lake. However, each firm must use

the lake's water in production, so it is also costly to

have a polluted lake. The cost to each firm of dealing with

water from a polluted lake is $1000 times the number of

polluting firms.

 

36. What is true about dominant strategies in the above game?

a. "Pollute" is a dominant strategy for both firms.

b. "Pollute" is a dominant strategy for Lago only.

c. "Don't Pollute" is a dominant strategy for both firms.

d. "Don't Pollute" is a dominant strategy for Lago only.

e. There are no dominant strategies.

37. What kind of game is being played by Lago and Nessie?

a. Battle of the Sexes.

b. Prisoners' Dilemma.

c. Beach Location.

d. Stackelberg Output Choice.

e. Cournot Output Choice.

 

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38. The equilibrium of this game, if played only once, is that

a. both firms pollute.

b. only Lago pollutes.

c. only Nessie pollutes.

d. neither firm pollutes.

e. the firms choose a mixed strategy.

39. If this game is repeated over an infinite or uncertain horizon, the most likely observed behavior will be that

a. both firms pollute.

b. only Lago pollutes.

c. only Nessie pollutes.

d. neither firm pollutes.

e. the firms alternate polluting in different periods.

40. A "mixed strategy" equilibrium means that

a. the strategies chosen by the players represent different behaviors.

b. one player has a dominant strategy, and one does not.

c. one player has a pure strategy, and one does not.

d. the equilibrium strategy is an assignment of probabilities to pure strategies.

e. the equilibrium strategy involves alternating between a dominant strategy and a Nash strategy.

For the following questions, consider the game below.

41. What is true about dominant strategies in the above game?

a. "Use more caffeine" and "have a sweepstakes" are dominant strategies.

b. "Use more caffeine" and "create a diet soda" are dominant strategies.

c. "Make animal-shaped bottles" and "have a sweepstakes" are dominant strategies.

d. "Make animal-shaped bottles" and "create a diet soda" are dominant strategies.

e. There are no dominant strategies.

42. The above game is

a. variable-sum.

b. constant-sum.

c. cooperative.

d. a Prisoners' Dilemma.

e. a Cournot Production Cross.

 

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43. Which of the below outcomes is the result of a Nash equilibrium in pure strategies for the above game?

a. -5, 5

b. 10, -10

c. 8, -8

d. 0, 0

e. There is no pure strategy equilibrium in this game.

44. In the above game, there is

a. a mixed strategy equilibrium, and no other.

b. a mixed strategy and a pure strategy equilibrium.

c. a mixed strategy and two pure strategy equilibria.

d. a mixed strategy and four pure strategy equilibrium.

e. no equilibrium in either mixed or pure strategies.

45. A "Credible Threat"

a. is also called a "tit-for-tat" strategy.

b. always set a low price.

c. minimizes the return of your opponent.

d. is a strategy selection that is in your best interest.

e. provides the best return for both players.

46. Repetition of a game

a. yields the same outcome, over and over.

b. can result in behavior that is different from what it would be if the game were played only once.

c. is not possible.

d. makes cooperative games into non-cooperative games.

e. is possible only if the payoffs in the matrix change.

47. The strategy that worked best in Axelrod's experiments using the Prisoners' Dilemma game was to

a. play the "cooperate" ("don't confess") strategy.

b. play the "defect" ("confess") strategy.

c. alternate between "cooperate" and "defect" strategies.

d. play the "cooperate" strategy at first, and from then on do whatever the other player did in the previous round, cooperating if the other player did, and defecting if the other player did.

e. play the "cooperate" strategy in the first round, and from then on cooperate so long as the other player does, but if the other player defects, then play the "defect" strategy from that time forward.

48. It can be rational to play tit-for-tat in a repeated Prisoners' Dilemma game

a. only if the game is played an infinite number of times.

b. if the game is played an infinite number of times, or if it is uncertain how many times it will be played.

c. only if the game is played a finite number of times, and that number is known by all the players in advance.

d. for n-1 of the n periods it will be played, if n is known in advance.

e. at no time; tit-for-tat is an irrational strategy in this situation.

 

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For the following questions, consider the game below.

49. What is true about dominant strategies in the above game?

a. R1 and C1 are dominant strategies.

b. R1 and C2 are dominant strategies.

c. R1 and C2 are dominant strategies.

d. R2 and C2 are dominant strategies.

e. There are no dominant strategies.

50. What kind of game is shown above?

a. Axelrod's Paradox.

b. Stackelberg Match.

c. Prisoners' Dilemma.

d. Cournot's Duopoly Game.

e. It is not possible to tell what kind of game it is because the strategies have not been identified.

51. In the game above, equilibrium is

a. R1, C1.

b. R1, C2.

c. R2, C1.

d. R2, C2.

e. a mixed strategy based on all four pure strategies.

52. When cost and demand are stable over time in an industry, repetition of Prisoners' Dilemma situations

a. can yield cooperative outcomes because firms can explicitly collude to set prices.

b. can yield cooperative outcomes even when firms do not explicitly collude to set prices.

c. cooperative or noncooperative outcomes may occur, but cooperation is harder than when the market is unstable.

d. will tend to yield noncooperative outcomes.

e. will always yield noncooperative outcomes.

53. Once the state environmental protection agency devises its new policy to protect the environment, firms decide whether to remain in the state or move their operations to a neighboring state. In the language of game theory, this is an example of:

a. a cooperative game.

b. a sequential game.

c. a threat.

d. the prisoners' dilemma.

 

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54. A "sequential game" is

a. another term for a repeated game.

b. another term for a cooperative game.

c. the term for a game in which individuals receive their payoffs at different times

d. the term for a game in which individuals do not commit to strategy choices at the same time.

e. the term for a game in which each outcome occurs, one after the other, as the game is repeated over time.

55. If a game has the same players, the same strategies, and the same possible outcomes, the equilibrium

a. may be different if it is a sequential game from what it would be if it were not.

b. must be different it is a sequential game from what it would be if it were not.

c. will be the same whether or not it is sequential.

d. is the same as the cooperative version of the game.

e. is the same as the noncooperative version of the game.

56. An oligopolistic situation involving the possible creation of barriers to entry would probably best be modeled by a

a. cooperative game.

b. Prisoners' Dilemma game.

c. Battle of the Sexes game.

d. repeated game.

e. sequential game.

57. What does it mean to say that a game is in "extensive form"?

a. Strategies are described, rather than just numbered.

b. All payoffs are shown.

c. The game is presented as a matrix.

d. The game is presented as a decision tree.

e. The game is written out as often as the situation calls for it to be played.

For the following questions, consider the game below.

58. Playing the above game sequentially would

a. not change the equilibrium.

b. change the equilibrium to (R1,C1).

c. change the equilibrium to (R2,C1) if R moved first.

d. change the equilibrium to (R2,C1) if C moved first.

e. change the equilibrium to (R2,C2).

 

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59. Playing the above game by using a maximin strategy would

a. not change the equilibrium.

b. change the equilibrium to (R1,C1).

c. change the equilibrium to (R2,C1) if R moved first.

d. change the equilibrium to (R2,C1) if C moved first.

e. change the equilibrium to (R2,C2).

60. If the Battle of the Sexes game were played sequentially,

a. one of the two pure strategy equilibria would become the only equilibrium.

b. the two pure strategy equilibria would alternate in being the equilibrium seen in each round of the game.

c. only the mixed strategy equilibrium would exist.

d. only the dominant strategy equilibrium would exist.

e. the equilibrium would not change.

For the following questions, consider the game below.

61. If the above game were not played sequentially,

a. the only equilibrium would be (R2,C1).

b. the only equilibrium would be (R1,C2).

c. the only equilibria would be (R2,C1) and (R1,C2)

d. the only equilibria would be (R2,C1), (R1,C2) and a mixed strategy.

e. there would not be any equilibrium.

62. Playing the above game sequentially would

a. not change the equilibrium.

b. change the equilibrium to (R1,C1).

c. change the equilibrium to (R2,C1) if R moved first.

d. change the equilibrium to (R2,C1) if C moved first.

e. change the equilibrium to (R2,C2).

63. What kind of game is shown above?

a. Battle of the Sexes.

b. Matching Pennies.

c. Prisoners' Dilemma.

d. The Product Choice game.

e. It is not possible to tell what kind of game it is because the strategies have not been identified.

 

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64. Which is true of output-choice models of oligopoly behavior?

a. Both the Stackelberg and Cournot models can be constructed as sequential games.

b. The Stackelberg, but not the Cournot, model can be constructed as a sequential game.

c. The Cournot, but not the Stackelberg, model can be constructed as a sequential game.

d. Neither the Cournot or the Stackelberg model can be constructed as a sequential game, but other output-choice models can be.

e. There is no relationship between any output-choice model and sequential games.

For the following questions, consider the game below.

65. The above game

a. is Stackelberg if both players move at the same time; Cournot if one player moves first.

b. is Cournot if both players move at the same time; Stackelberg if one player moves first.

c. Stackelberg no matter what the timing of moves.

d. Cournot no matter what the timing of moves.

e. is neither Stackelberg nor Cournot.

66. In the above game,

a. R's dominant strategy is Q = 100; C has none.

b. C's dominant strategy is Q = 100; R has none.

c. Q = 100 is a dominant strategy for both R and C.

d. Q = 100 dominates Q =150 for both firms.

e. the dominant strategy for both players is to choose the same level of output, so long as it is not 150.

67. What is true of equilibrium in the above game?

a. In equilibrium, both firms choose Q = 50.

b. In equilibrium, both firms choose Q = 100.

c. There are two equilibria, at Q = 50 and at Q = 100.

d. The only equilibrium is in mixed strategies.

e. The two equilibria are those associated with the (40,30) outcome and the (30,40) outcome.

 

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68. In the above game, each firm has a strategy that would not be chosen under any circumstances. This strategy is

a. Q = 50.

b. Q = 100.

c. Q = 150.

d. "choose the same Q as the other player."

e. "choose a Q different from the other player's."

69. When, in the above game, the strategy that would not be chosen under any circumstances is removed, what is left is a

a. Battle of the Sexes game.

b. Matching Pennies game.

c. Prisoners' Dilemma game.

d. Beach Location game.

e. constant-sum game.

70. If, in the above game, R moves first, it will select

a. Q = 50.

b. Q = 100.

c. Q = 150.

d. a mixed strategy over the three choices that includes some positive likelihood for each Q.

e. a mixed strategy over the choices Q = 50 and Q = 100.

71. If, in the above game, R moves first, C will respond with

a. Q = 50.

b. Q = 100.

c. Q = 150.

d. a mixed strategy over the three choices that includes some positive likelihood for each Q.

e. a mixed strategy over the choices Q = 50 and Q = 100.

72. Relative to a simultaneous-move situation, the gain to firm R from being able to move first in the above game would be

a. 40.

b. 37.

c. 32.

d. 5.

e. 3.

73. Relative to a simultaneous-move situation, the loss to firm C from having to move second in the above game would be

a. 37.

b. 20.

c. 12.

d. 8.

e. 5.

74. If player R moves first in the above game, equilibrium will

a. not be different from what it is in the simultaneous-move scenario.

b. be to R's detriment because it will not be able to react to C's choice.

c. be one in which R chooses 50 and C chooses 150.

d. be one in which R chooses 100 and C chooses 50.

e. be one in which R chooses 150 and C chooses 50.

 

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75. Wal-Mart was one of the most successful firms of the '70s and '80s. Much of Wal-Mart's success can be credited to its expansion strategy: they rushed to open the first discount store in small towns that could only support one discount store. In the language of game theory:

a. Wal-Mart was a dominant firm.

b. Wal-Mart made empty threats.

c. Wal-Mart employed a maximin strategy.

d. Wal-Mart employed a preemptive strategy.

76. As defined by Thomas Schelling, a "strategic move" is

a. any strategy choice in a game.

b. any strategy choice consistent with Nash equilibrium.

c. any strategy choice in a sequential game.

d. a strategy choice that influences the subsequent strategy choice of another player.

e. a strategy choice that restricts the set of outcomes available to another player.

For the following questions, consider the pricing game below.

77. Which is true about dominant strategies in the above game?

a. $80 is dominant for Simple; $70 is dominant for Boring.

b. $80 is dominant for Simple; $25 is dominant for Boring.

c. $35 is dominant for Simple; $70 is dominant for Boring.

d. $35 is dominant for Simple; $25 is dominant for Boring.

e. There are no dominant strategies in the above game.

78. If the firms price simultaneously, equilibrium would be

a. an $80 price for Simple and a $70 price for Boring.

b. an $80 price for Simple and a $25 price for Boring.

c. a $35 price for Simple and a $70 price for Boring.

d. a $35 price for Simple and a $25 price for Boring.

e. a mixed strategy equilibrium.

79. If Simple were able to move first, equilibrium would be

a. an $80 price for Simple and a $70 price for Boring.

b. an $80 price for Simple and a $25 price for Boring.

c. a $35 price for Simple and a $70 price for Boring.

d. a $35 price for Simple and a $25 price for Boring.

e. a mixed strategy equilibrium.

 

Page 17

80. If Boring were able to move first, equilibrium would be

a. an $80 price for Simple and a $70 price for Boring.

b. an $80 price for Simple and a $25 price for Boring.

c. a $35 price for Simple and a $70 price for Boring.

d. a $35 price for Simple and a $25 price for Boring.

e. a mixed strategy equilibrium.

81. What is true about threats in the above game?

a. Simple can change the equilibrium by means of a credible threat; Boring cannot.

b. Boring can change the equilibrium by means of a credible threat; Simple cannot.

c. Boring can change the equilibrium by means of a credible threat only if it can move before Simple.

d. Simple can change the equilibrium by means of a credible threat only if it can move before Boring.

e. Neither firm has a credible threat with which to change this equilibrium.

For the following questions, consider the pricing game below.

82. What is true about dominant strategies in the above game?

a. Gelato is a dominant strategy for both firms.

b. Yogurt is a dominant strategy for Gooi only.

c. Yogurt is a dominant strategy for Ici only.

d. Yogurt is a dominant strategy for both firms.

e. There are no dominant strategies in the above game.

83. If the firms must choose their prices simultaneously,

a. both firms will buy gelato.

b. both firms will buy yogurt.

c. two pure strategy equilibria exist, one in which Gooi alone buy gelato and one in which Ici alone buys gelato.

d. the game has no pure strategy equilibrium.

e. the game has no mixed strategy equilibrium.

84. If Gooi moves first, the payoff in equilibrium will be

a. $150, $0.

b. $150, $300.

c. $400, $150.

d. $50, $50.

e. $650, $450.

 

Page 18

85. If Gooi can move first, and Ici threatens to buy yogurt machines, no matter what Gooi does,

a. Gooi will have to buy gelato machines, so Ici will get its highest possible profit.

b. Gooi will buy yogurt machines, which it otherwise wouldn't have, in order to retaliate.

c. the equilibrium payoff of ($50,$50) will be enforced.

d. Gooi will not change its behavior, because Ici's threat is not credible.

e. Gooi will threaten to buy yogurt machines, no matter what Ici does, to see whether that will get the people at Ici to change their minds.

86. If Gooi can move first, and Ici wants to realize the ($150, $300) payoff,

a. all it has to do is threaten to buy yogurt machines, no matter what Gooi does.

b. it could make its threat credible by rearranging its physical plant so that the installation of gelato machines would bring in profit less than $50.

c. it could make its threat credible by rearranging its physical plant so that the installation of gelato machines would bring in profit less than $150.

d. it could make its threat credible by rearranging its physical plant so that the installation of gelato machines would bring in profit less than $300.

e. it has to move before Gooi; there is no other way.

87. La Tortilla is the only producer of tortillas in Santa Teresa. The firm produces 10,000 tortillas each day and has the capacity to increase production to 100,000 tortillas each day. La Tortilla has made a large profit for years, but no other firm has chosen to compete in the Santa Teresa tortilla market. La Tortilla has been able to deter entry because if other firms were to enter the market it would greatly step-up production and reduce price.

a. La Tortilla's behavior is inconsistent with economic theory.

b. La Tortilla has been successful because of its credible threat.

c. La Tortilla behaves like a Stackelberg firm.

d. La Tortilla must have other barriers to entry to protect its monopoly power.

 

Page 19

For the following questions, consider the entry-deterrence game below. The potential entrant would have to spend some amount in sunk costs to enter the market.

88. In the above game, who moves first?

a. Potential Entrant

b. Incumbent Monopoly

c. It's a sequential game; firms alternate moving first.

d. Both players move simultaneously.

e. Who moves first is decided by the equilibrium.

89. In the above game, Incumbent Monopoly has

a. an incentive to threaten accomodation, which would be credible.

b. an incentive to threaten war, which would be credible.

c. an incentive to threaten accomodation, which wouldn't be credible.

d. an incentive to threaten war, which wouldn't be credible.

e. no incentive to make a threat.

90. If the game above were to be infinitely repeated, waging a price war might be a rational strategy

a. because there would be no short-term losses.

b. because the short-term losses might be outweighed by long-term gains from preventing entry.

c. if the potential entrant were irrational.

d. if the monopolist had excess capacity.

e. if there were no sunk costs to the potential entrant.

91. If the Incumbent Monopoly installed excess capacity in advance of the Potential Entrant's appearance on the scene, and this excess capacity had a cost of $X, it would reduce by $X the Incumbent Monopoly's payoffs in the

a. top row.

b. bottom row.

c. left column.

d. right column.

e. entire matrix.

 

Page 20

92. Your firm needs a private investigator and the best private eye in Santa Teresa is Kinsey Milhone. Her services are worth $30,000 to your firm but you do not want to pay her more than $10,000. You tell Kinsey that you cannot pay her more than $10,000 unless you get prior approval from the Board of Directors of your company, and, unfortunately, they just met and won't meet again for 6 months. This strategic move on your part gives you _____ flexibility and _____ bargaining power.

a. less, less

b. less, more

c. more, less

d. more, more

93. In a two person bargaining situation

a. always in the best interests of both players for each player to be as flexible as possible, and to have as many options as possible.

b. always in the best interest of the player that moves first to be as flexible as possible, and to have as many options as possible.

c. often in the best interest of players to pretend a game is noncooperative when it is not, and vice versa.

d. often in the best interest of players to cut off some of their own options in order to make the other player's threats not credible.

e. often in the best interest of players to cut off some of their own options in order to make their own threats credible.

94. Buy-Right is a chain of grocery stores operating in small cities throughout the southwestern United States. Buy-Right'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. Buy-Right'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?

 

Page 21

95. Two firms at the St. Louis airport have franchises to carry passengers to and from hotels in downtown St. Louis. These two firms, Metro Limo and Urban Limo, operate nine passenger vans. These duopolists cannot compete with price, but they can compete through advertising. Their payoff matrix is below:

a. Does each firm have a dominant strategy? If so, explain and what

that strategy is.

b. What is the Nash equilibrium? Explain where the Nash equilibrium

occurs in the payoff matrix.

96. Consider two firms, X and Y, that produce super computers. Each can produce the next generation super computer for the military (M) or for civilian research (C). However, only one can successfully produce for both markets simultaneously. Also, if one produces M, the other might not be able to successfully produce M, because of the limited market. The following payoff matrix illustrates the problem.

a. Find the Nash equilibrium, and explain why it is a Nash

equilibrium.

b. If Firm X were unsure that the management of Firm Y were

rational, what would Firm X choose to do if it followed a

maximin strategy? What would both firms do if they both followed

a maximin strategy?

 

Page 22

97. G.C. Donovan Company is a large pharmaceutical company located in the U.S., but with worldwide sales. Donovan has recently developed two new medications that have been licensed for sale in European Common Market countries. One medication is an over-the-counter cold preparation that effectively eliminates virtually all cold symptoms, while the other is an antibiotic that is effective against drug resistant bacteria. A European firm, Demtech Limited, has developed drugs that are similar to Donovan's and will be ready for the European market at approximately the same time. Liability concerns make it unlikely that either firm will choose to market both new drugs at this time. Both firms do plan to market one of the drugs this year. Donovan's managers consider their own lack of reputation among European physicians to be an important obstacle in the antibiotic market. Consequently, Donovan feels more comfortable marketing the cold preparation. Demtech, on the other hand, has an excellent reputation among physicians but little experience in over the-counter drugs so that Demtech's competitive advantage is with the antibiotic. Should Demtech choose to market the cold remedy, they believe that their sales will increase if Donovan also enters the cold remedy market and advertises heavily. Similarly, Donovan anticipates that their sales in the antibiotic market would be enhanced if Demtech produces antibiotics, given Demtech's excellent reputation among physicians. In short, each firm believes that there are circumstances under which participation by the other firm will complement rather than compete with the firm's own sales. Profits in millions of dollars are given in the payoff matrix below.

a. Given the table above, does either firm have a dominant strategy?

Is there a Nash equilibrium? (Explain the difference between a Nash

equilibrium and a dominant strategy.)

b. Pharmaceutical firms within the EEC are attempting to organize a

risk pool that would share liability risks for new drugs. Since

Donovan and Demtech are among the largest pharmaceutical companies

operating in Europe, the benefits of the risk pool depend upon the

participation of the other firm. Increased profit achieved through

reduced risk liability (measured in millions of dollars) are shown

in the payoff matrix below.

c. Does either firm have an incentive to use participation in the risk

pool as a bargaining device in the drug-marketing decision? If so,

what would be the nature of the bargain? How credible is the firm's

Page 23

bargaining position? What could be done to make the bargaining

position more credible?

98. The widget market is controlled by two firms: Acme Widget Company and Widgetway Manufacturing. The structure of the market makes secret price cutting impossible. Each firm announces a price at the beginning of the time period and sells widgets at the price for the duration of the period. There is very little brand loyalty among widget buyers so that each firm's demand is highly elastic. Each firm's prices are thus very sensitive to inter-firm price differentials. The two firms must choose between a high and low price strategy for the coming period. Profits (measured in thousands of dollars) for the two firms under each price strategy are given in the payoff matrix below. Widgetway's profit is before the comma, Acme's is after the comma.

a. Does either firm have a dominant strategy? What strategy should

each firm follow?

b. Would an assumption that the game is to be played an infinite

number of times affect your answer regarding the appropriate

strategy? If so, what strategy is appropriate with an infinite

number of games?

c. Assume that the game is to be played a very large (but finite)

number of times. What is the appropriate strategy if both firms are

always rational?

 

Page 24

99. Mitchell Electronics produces a home video game that has become very popular with children. Mitchell's managers have reason to believe that Wright Televideo Company is considering entering the market with a competing product. Mitchell must decide whether to set a high price to accomoderateate entry or a low, entry detering price. The payoff matrix below shows the profit outcome for each company under the alternative price and entry strategies. Mitchell's profit is entered before the comma, Wright's is after the comma.

a. Does Mitchell have a dominant strategy? Explain.

b. Does Wright have a dominant strategy? Explain.

c. Mitchell's managers have vaguely suggested a willingness to lower

price in order to deter entry. Is this threat credible in light of

the payoff matrix above?

d. If the threat is not credible, what changes in the payoff matrix

would be necessary to make the threat credible? What business

strategies could Mitchell use to alter the payoff matrix so that

the threat is credible?

100. The countries Economus and Sociolomous on planet Subjectus are engaged in a Cold War. The pay-offs of their available strategies are presented in the table below.

The pay-offs are listed in terms of percentage growth in the

standard of living of the two countries. Does either country have

a dominant strategy? Does the game have a Nash equilibrium? What

is the maxmin strategy of each player in the game?

 

Page 25

101. Megan and Amanda are both 7 years old and operate lemonade stands. Megan lives on the east side of Welch while Amanda resides on the west side of the north-south street. Each morning, the girls must decide whether to place their stand on Welch Avenue or Lincoln. When they set their stand-up, they don't know what the other will do and can't relocate. If both girls put their stand on Welch, both girls receive $175 in profits. If both girls put their stand on Lincoln, they each receive $75 in profits. If one girl sets her stand on Welch while the other operates on Lincoln, the stand on Welch earns $300 in profits while the stand on Lincoln earns $225. Diagram the relevant pay-off matrix. Does either girl have a dominant strategy? Does the game have a Nash equilibrium? What is the maxmin strategy of each player in the game?

102. Dale and Terry are racing automobiles around a track. Currently, Terry is in the lead, however, Dale has a faster car and is just behind Terry. The racers' strategies and pay-offs are presented in the table below.

Does either player have a dominant strategy? Does the game have a Nash equilibrium? What is the maxmin strategy of each player in the game?

 

Page 26

103. Dale and Terry are racing automobiles around a track. Currently, Terry is in the lead, however, Dale has a faster car and is just behind Terry. The racers' strategies and pay-offs are presented in the table below. The goal of the drivers is to finish as high as possible. There are a total of 43 cars on the track.

Does either player have a dominant strategy? Does the game have a Nash

equilibrium? What is the maxmin strategy of each player in the game?

104. Tony and Larry are managers of baseball teams currently competing. It's late in the ballgame and Tony's team is currently winning and in the field. Tony's strategies are bring in a righthanded pitcher (RHP) or bring in a lefthanded pitcher (LHP). Larry's strategies are bring in a righthanded pinch hitter (RPH) or bring in a lefthanded pinch hitter (LPH). The pay-off matrix is in terms of winning (W) or losing (L) the game. Does either player have a dominant strategy? Does the game have a Nash equilibrium? What is the maxmin strategy of each player in the game?

Page 27

105. Casey's General Store is considering placing a store in Hamilton, Missouri. If they place the store in Hamilton and no other convenience store enters the Hamilton market, they'll earn profits of $100,000 per year. If competitors do enter, Casey's profits as well as the competitor's profits will be reduced to $0 per year. If a competitor enters the Hamilton market and Casey's does not, the competitors profits will be $100,000 per year.

Does either player have a dominant strategy? Does the game have any Nash equilibrium(s)? What is the maxmin strategy of each player in the game?

106. Gym X and Bodyworks are both going to open an exercising facility in the local market. Each company may decide to open a facility concentrating on cardio equipment for customers interested in mostly aerobic workouts. Another alternative for each company is to open a facility concentrating on muscle building equipment for customers interested mostly in bodybuilding workouts. The pay-off matrix for each company dependent upon their strategies and that of their competitor is given below.

Does either player have a dominant strategy? Does the game have any Nash equilibrium(s)? What is the maxmin strategy of each player in the game?

Page 28

107. Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will engage in product research to innovate their version of the cyberwidget. The pay-offs of each firms strategy is a function of the strategy of their competitor as well. The pay-off matrix is presented below.

Does either player have a dominant strategy? Does the game have any Nash equilibrium(s)? What is the maxmin strategy of each player in the game?

108. A small regional airline is considering offering service to the Big City market. A large carrier already provides service to Big City. The small carrier's two strategies are: Enter Market or Do Not Enter. The large carrier's strategies are: Price Dump or Maximize Profits in the Short Run. By price dumping in the Big City market, the large carrier can force the small carrier out of business and make monopoly profits in the long-run. The long-run pay-offs are presented in the pay-off matrix below.

Does either player have a dominant strategy? Does the game have any Nash equilibrium(s)? What is the maxmin strategy of each player in the game?

 

Page 29

109. Joanna has a credit card account with Card Bank. Card Bank's available strategies are raise Joanna's credit card interest rate or do nothing. Joanna's available strategies are transfer her Card Bank account balance to another creditor or do nothing. The strategy pay-offs are indicated below.

Does either player have a dominant strategy? Does the game have any Nash equilibrium(s)? What is the maxmin strategy of each player in the game?

110. Joanna has a credit card account with Card Bank. Card Bank's available strategies are raise Joanna's credit card interest rate or do nothing. Joanna's available strategies are transfer her Card Bank account balance to another creditor or do nothing. If Card Bank raises Joanna's interest rate and Joanna does nothing, Card Bank increases profits by $1,000 while Joanna receives $-1,000. If Card Bank raises Joanna's interest rate and Joanna transfers her account to another creditor, Card Bank receives $-300 while Joanna receives $-100. If Card Bank does nothing and Joanna does nothing, each player receives $0. If Card Bank does nothing and Joanna transfers her account to another creditor, Card Bank receives $-300 while Joanna receives $-150. Diagram the game tree for this sequential game. Indicate any Nash equilibrium(s).

 

Page 30

111. Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will engage in product research to innovate their version of the cyberwidget. The pay-offs of each firm's strategy is a function of the strategy of their competitor as well. The pay-off matrix is presented below.

Firm #2 chooses to innovate with probability 20/21. If Firm #1 does the same, what is the expected pay-off? Is this a Mixed Strategy Nash Equilibrium? Suppose, instead, that firm #2 innovates with probability 2/3. Should player #1 always innovate?

112. Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will offer a warranty or not. The pay-offs of each firm's strategy is a function of their competitor as well. The pay-off matrix is presented below.

Does either player have a dominant strategy? Does the game have any Nash equilibrium(s)? What is the maxmin strategy of each player in the game? Should the players use a mixed strategy?

Page 31

113. Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will offer a warranty or not. The pay-offs of each firm's strategy is a function of their competitor as well. The pay-off matrix is presented below.

If firm #1 announces they will offer a warranty regardless of what firm #2 does, is this a credible threat? Why or why not?

114. Two firms in a local market compete in the manufacture of cyberwidgets. Each firm must decide if they will offer a warranty or not. The pay-offs of each firm's strategy is a function of their competitor as well. The pay-off matrix is presented below.

If firm #1 announces they will offer a warranty regardless of what firm #2 does, is this a credible threat? Why or why not?

Page 1

1. c

2. b

3. a

4. a

5. e

6. c

7. b

8. b

9. c

10. a

11. c

12. e

13. a

14. c

15. a

16. e

17. e

18. e

19. c

20. a

21. a

22. c

23. b

24. d

25. e

26. a

27. b

28. b

29. d

30. e

31. d

32. c

33. d

34. d

35. c

36. a

37. b

38. a

39. d

40. d

41. e

42. b

43. e

44. a

45. d

46. b

47. d

48. b

49. d

50. c

51. d

52. b

53. b

54. d

55. a

Page 2

56. e

57. d

58. a

59. a

60. a

61. d

62. c

63. d

64. b

65. b

66. d

67. b

68. c

69. c

70. c

71. a

72. d

73. c

74. e

75. d

76. d

77. b

78. b

79. b

80. b

81. e

82. e

83. c

84. c

85. d

86. b

87. b

88. a

89. d

90. b

91. e

92. b

93. e

94. a. A dominant strategy is one that is optimal regardless of the rival

strategy.

b. For both firms, the dominant strategy is to increase advertising.

If Acme increases advertising, Buy-Right earns 20 by increasing, 2

by not increasing.

Profit is higher for Buy-Right by increasing, regardless of Acme's

choice.

The same can be shown to be true for Acme.

c. Either or both firms would not have a dominant strategy if their

best choice depended on the choice of their rival.

Page 3

95. a. Firm A has no dominant strategy. If B advertises, then A does

best by advertising; but if B does not advertise, then A should

not advertise. Firm B has a dominant strategy, and it should

advertise.

b. The Nash equilibrium is for both firms to advertise. Each does

best, 25 and 15, respectively, by advertising, given what the

other firm does.

96. a. The Nash equilibrium occurs at the bottom right on the C,C

position. In this position, each firm does its best given what

the other firm does.

b. Firm X would find the maximum of the minimum payoffs. If Firm X

chose M, the minimum payoff for X would be 2. If Firm X chose C,

then the minimum payoff for X would be 1. Thus, the maximum

would be 2. Firm X should choose M. If both firms followed a

maximin strategy, then the top right corner 2,2 would by the

outcome.

97. a. Demtech has a dominant strategy in the cold preparation since

Demtech is better off producing the cold remedy regardless of

Donovan's choice. The Nash equilibrium is for both firms to produce

the cold remedy. We can deduce this from Demtech's dominant

strategy. Given that Demtech will produce the cold remedy, Donovan

should also produce the cold remedy. (Donovan's dominant strategy

is also to produce the cold remedy.)

b. Dominant Strategy: A strategy that is optimal regardless of rival's

strategy. Nash equilibrium: A strategy that a player believes is

optimal, given the rival strategy.

c. Donovan should bargain to tie participation in the risk pool to a

commitment from Demtech to produce the antibiotic. Donovan's

position is fairly credible because they gain more profit if

Demtech agrees (40 million) than they lose (15 million at most) by

refusing to participate in the pool. Donovan can make their

position more credible by making their intentions public and by

always sticking to their guns.

98. a. Each firm's dominant strategy is the low price. This follows form

the realization that each player is better off with the low price

strategy regardless of the opponent's strategy.

b. With an infinite number of trials, a tit-for-tat strategy is

appropriate. Under tit-for-tat, each player chooses the high price

so long as his rival cooperates by also choosing the high price.

Once the rival cuts prices, the other player retaliates. If the

rival raises price back to the high price, the firm follows suit.

c. A finite number of periods implies a low price for every period.

The process begins when each player realizes their opponent cannot

retaliate after the last period so that the low price is rational

for the last period. This in turn makes the low price rational for

the next to last period and so on.

Page 4

99. a. Mitchell's dominant strategy is the high price. Regardless of

Wright's decision to enter, Mitchell earns a larger profit with a

high price.

b. Wright does not have a dominant strategy. Wright's best choice

depends upon the decision made by Mitchell. When Mitchell sets a

high price, Wright should enter, whereas a low Mitchell price leads

to no entry.

c. Mitchell's threat is not credible. It is obvious that Mitchell's

best strategy is to set a high price, regardless of the decision

Wright makes regarding entry.

d. To make the threat credible, Mitchell's best strategy must be the

low price, at least for the case where Wright enters. A possible

business strategy would be for Mitchell to expand capacity,

increasing the profit maximizing quantity.

100. Both countries can do better by continuing the Arms Build-up

regardless of what their competitor chooses. Thus, both countries

have a dominant strategy to continue the Arms Build-up. The Nash

Equilibrium is the cell corresponding to both countries choosing

the "Continue Arms Build-up" strategy. The maxmin strategy will

avoid the players losing 50 percent growth in the standard of

living. To avoid this outcome, the players must choose the Continue

Arms Build-up Strategy.

101. Neither player has a dominant strategy in this game. There are two

Nash equilibriums in this game. The first Nash equilibrium is where

Megan places her stand on Welch while Amanda places her stand on

Lincoln. The second Nash equilibrium occurs where Megan places her

stand on Lincoln while Amanda places her stand on Welch. The maxmin

strategy for both players will be to avoid the $75 pay-off. To do

this, the player will never choose to locate on Lincoln. If both

players due this, the result will be for both players locating on

Welch.

旼컴컴컴컴컴컴컴컫컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴컴

Megan

냐컴컴컴컴컴컴컴컴컴컴컴컫컴컴컴컴컴컴컴컴컴컴컴컴캐

Welch Lincoln

냐컴쩡컴컴컴컴컴콰컴컴컴컴컴컴컴컴컴컴컴컴遂컴컴컴컴컴컴컴컴컴컴컴컴

A

m Welch 175, 175 300, 225

a

n 냐컴컴컴컴컴콰컴컴컴컴컴컴컴컴컴컴컴컴遂컴컴컴컴컴컴컴컴컴컴컴컴

d

a Lincoln 225, 300 75, 75

읕컴좔컴컴컴컴컴컨컴컴컴컴컴컴컴컴컴컴컴컴좔컴컴컴컴컴컴컴컴컴컴컴컴

102. Neither player has a dominant strategy. Also, there is no Nash equilibrium in this game. There is no strategy the player can choose to prevent the worst outcome. Thus, there is no maxmin strategy.

103. Neither player has a dominant strategy. Also, there is no Nash equilibrium in this game. Each player can play the "Do Nothing" strategy to avoid a finish out of the top 2. Thus, the "Do Nothing" strategy is the maxmin strategy for both players.

Page 5

104. Neither player has a dominant strategy in this game. Also, there is no Nash equilibrium. Neither player has a maxmin strategy available as they cannot avoid a chance at losing.

105. Both players can do at least as well or better by playing the "ENTER" option regardless of what their competitor does. This implies both players have a dominant strategy of "ENTER." The dominant strategy equilibrium is for both players to play "ENTER." This is not the only Nash equilibrium. This game has three Nash equilibriums. The only cell that is not a Nash equilibrium is the cell corresponding to both players playing the "DO NOT ENTER" strategy. Given Casey's will not enter the market, the Competitor's best strategy is to enter the market (and vice versa). For both players, neither strategy offers a path to maximize the minimum gain as the minimum gain is equivalent for all strategies.

106. Neither player has a dominant strategy in this game. There are two Nash equilibriums. A Nash equilibrium corresponds to Gym X choosing the "Cardio" strategy while Bodyworks chooses the "Muscle Building" strategy. Another Nash equilibrium corresponds to Bodyworks choosing the "Cardio" strategy while Gym X chooses the "Muscle Building" strategy. Each player's maxmin strategy would be to avoid the -$15 outcome. Thus, the maxmin strategy is for each player to choose the "Cardio" strategy.

107. Neither player has a dominant strategy in this game. There are two Nash equilibriums in this game. One Nash equilibrium is for Firm #1 to Innovate their product while Firm #2 does not. A second Nash equilibrium is for Firm #2 to Innovate their product while Firm #1 does not. Each player's maxmin strategy is to choose the "DO NOT INNOVATE" option.

108. Neither player has a dominant strategy in this game. Also, there is no Nash equilibrium in the game. The small carrier's maxmin strategy is to choose the "DO NOT ENTER" option. The large carrier's maxmin strategy is to choose the "PRICE DUMP" strategy.

109. Card Bank's can always do at least as well or better by choosing the "Raise" strategy. This implies that Card Bank's dominant strategy is to raise Joanna's interest rate. Joanna does not have a dominant strategy. The Nash equilibrium in this game corresponds to Joanna transferring her balance to another creditor while Card Bank raises Joanna's interest rate. Joanna's maxmin strategy is to Transfer to another creditor. Card Bank has no maxmin strategy as the bank cannot avoid the $-300 outcome by choosing a particular strategy.

110. The Nash equilibrium is for both players to choose the "Do Nothing" strategy. The game tree is indicated below.

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111. If firm #1 does the same, expected pay-offs for both firms are zero. This is a Mixed Strategy Nash Equilibrium. If Firm #2 chooses to innovate with probability 2/3, Firm #1 should always innovate. This is because expected profits are as high as possible when firm #1 sets the probability of choosing to innovate equal to 1.

112. Both players have a dominant strategy to offer a warranty on their cyberwidgets. This implies the game has a dominant strategy equilibrium of both firms offering a warranty. This is also the only Nash equilibrium in the game. Each player's maxmin strategy is to avoid the -$10 outcome. To avoid this outcome, both player's maxmin strategy is to "Offer Warranty." The players do best by choosing to Offer a Warranty regardless of what their opponent does. Thus, the optimal mixed strategy is to set the probability of offering a warranty equal to one.

113. Both firms offering a warranty and both firms offering no warranty are both Nash Equilibriums for this game. Firm #1 prefers the Nash Equilibrium corresponding to both firms offering a warranty on their cyberwidgets. Firm #1's announcement is a credible threat. Firm #1 actually can always do at least as well or better by offering a warranty. Thus, firm #1's dominant strategy is to offer a warranty.

114. Both firms offering a warranty and both firms offering no warranty are both Nash Equilibriums for this game. Firm #1 prefers the Nash Equilibrium corresponding to both firms offering a warranty on their cyberwidgets. Firm #1's announcement is not a credible threat. Firm #1 actually can do better by not offering a warranty given firm #2 does not offer a warranty. Thus, it is in firm #1's best interest to not offer a warranty if firm #2 does not offer a warranty regardless of firm #1's announcement.