Practice Questions #10
1) Game theory, when applied to an oligopoly situation,
a) illustrates the tension between self-interest and cooperation.
b) relies on the logic of firms pursing their own self-interests.
c) relies on the notion that each firm chooses its best strategy, given the strategies that other firms have chosen.
d) All of the above are correct.
2) (This question relies on the text) In a duopoly situation (this is, when there are only two firms in a market), the logic of self-interest results in a total output level that
a) equals the output level that would prevail in a competitive market.
b) equals the output level that would prevail in a monopoly.
c) exceeds the monopoly level, but falls short of the competitive level.
d) Is less than the monopoly level.
3) As the number of firms in an oligopoly market
a) decreases, the market approaches a cartel equilibrium.
b) decreases, the market approaches a competitive market equilibrium.
c) increases, the market approaches a competitive market equilibrium.
d) increases, the market approaches a monopoly market equilibrium.
4) As the number of firms in an oligopoly grows larger, the price approaches
a) zero.
b) marginal cost.
c) infinity.
d) the monopoly price.
5) Consider the following table. In this game each participant has to decide whether to go (G) or not (NG) to the cinema. In each cell you have the payoff of each player if the game ends in such a position (the first value is Ivan's payoff and the second value is Jennifer Aniston's payoff)
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Jennifer Aniston
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Ivan
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G
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NG
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|
G
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(4, 3)
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(-4, 0)
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NG
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(0, -1)
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(0,0)
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a) T or F. Ivan should play G because is a dominant strategy for him.
b) T or F. There are no dominant strategies in this game.
c) T or F. This game has an equilibrium.
6) What is the dominant strategy for each player in the following games?
a)
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P1
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P2
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|
|
UP
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Down
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Up
|
0,0
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4,6
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|
Down
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12,2
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0,8
|
b)
| P2 |
| P1 |
|
D |
E |
F |
| A |
6,1 |
47,12 |
5,0 |
| B |
3,15 |
35,17 |
0,8 |
| C |
0,10 |
7,12 |
3,7 |
7) Two cigarette manufacturers (Firms A and Firm B) are faced with lawsuits from the states to recover the health care related expenses associated with cigarette smoking (like cancer and other illness). Each firm has been presented with an opportunity to lower their liability in the suit if they cooperate with attorneys representing the state. If firm A concedes that cigarette smoke causes lung cancer while Firm B does not concede, then A's payment will be $5 and B's payment will be $50. If firm A argues that there is no evidence that smoke causes cancer but B does argues this, then A's payment will be $50 and B's payment will be $5. If, on the other hand, both firms argue that there is no evidence, the payment will be $10 for each firm. Finally, if both firms concede that smoke causes cancer, A's payment is $20 and B's payment is $15.
a) Set up the payoff matrix for this game using the following table. (HINT: take into account that the payments made by firms will be negative numbers inside the matrix since they represent an expenditure)
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Firm B
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Firm A
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Concede
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No evidence
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Concede
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|
|
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No evidence
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|
|
b) Pursing its own best interests, Firm A will concede that cigarette smoke causes lung cancer
I. only if firm B concedes that cigarette smoke causes lung cancer.
II. only if firm B does not concede that cigarette smoke causes lung cancer.
III. regardless of whether Firm B concedes that cigarette smoke causes lung cancer.
IV. none of the above; in pursing its own best interest, Firm A will in no case concede that cigarette smoke causes lung cancer.
c) Pursing its own best interests, Firm B will concede that cigarette smoke causes lung cancer
I. only if firm A concedes that cigarette smoke causes lung cancer.
II. only if firm A does not concede that cigarette smoke causes lung cancer.
III. regardless of whether Firm A concedes that cigarette smoke causes lung cancer.
IV. none of the above; in pursing its own best interest, Firm B will in no case concede that cigarette smoke causes lung cancer.
d) This particular game
I. features a dominant strategy for Firm A.
II. features a dominant strategy for Firm B.
III. is a version of the prisoners dilemma game.
IV. All of the above are correct.
e) In both firms follow a dominant strategy, Firm A's profits (losses) will be
I. $ -50
II. $ -20
III. $ -10
IV. $ -5
8) Roberto and Ruben are the only two guys that sell Brats to the crowd during Badgers' games. The market demand is given by the equation Q = 22 - 2P and Budgers' fans buy Brats from the guy with the lowest price. If Roberto and Ruben charge the same price, half the crowd go to each shop. In addition, the cost of producing one Brat is $1 for each guy (assume there are no fixed costs). Both guys set their prices simultaneously.
a) What is the joint profit-maximizing price (i.e., what price would Roberto and Ruben charge if they were able to collude and split the production between them)? What profit would each guy make if they set this price?
b) Suppose Ruben and Roberto compete by simultaneously choosing prices and can set either the joint profit maximizing price in part a) or can charge $1 less (let's say, cheat). What are profits if both Ruben and Roberto decide to charge $1 less? What are the profits if only one of them decided to cheat and charge $1 less?. Fill in the following matrix for the profits of the two sellers.
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Roberto
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Ruben
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Collude
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Cheat
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Collude
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|
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Cheat
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|
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c) What price will each firm charge in the equilibrium for this game? (Note that Ruben and Roberto can either cheat or collude, but there are no other options for them).
EXTRA EXERCISE
10) Consider the following game.
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Walk
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Bike
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Car
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Go
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3, 1
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W,85
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5,7
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Stay
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26,6
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4,4
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1,0
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Look at the following definition. An Equilibrium is a situation in which EACH player choose its best strategy given the strategy the other player have chosen. With this definition, answer the following questions.
a) For what values of W is (Go, Bike) an Equilibrium?
a. W = 4
b. W < 4
c. W > 4
d. W = 0
e. Any value of W
b) For what values of W is (Stay, Walk) an Equilibrium?
a. W = 4
b. W < 4
c. W > 4
d. W = 0
e. Any value of W