Download PROBLEM SET #7 1. A dominant strategy is a strategy that A. results

PROBLEM SET #7
1. A dominant strategy is a strategy that
A. results in the highest payoff to a player regardless of the opponent's action.
B. guarantees the highest payoff given the worst possible scenario.
C. describes a set of strategies in which no player can improve her payoff by unilaterally
changing her own strategy, given the other players' strategies.
D. whereby a player randomizes over two or more available actions in order to keep rivals from
being able to predict her action.
2. Consider the following information for a simultaneous move game: If you advertise and your
rival advertises, you each will earn $5 million in profits. If neither of you advertise, you will each
earn $10 million in profits. However, if one of you advertises and the other does not, the firm
that advertises will earn $15 million and the non advertising firm will earn $1 million. If you and
your rival plan to hand your business down to your children (and this "bequest" goes on forever)
then a Nash equilibrium when the interest rate is zero is
A. for each firm to not advertise until the rival does, and then to advertise forever.
B. for your firm to never advertise.
C. for your firm to always advertise when your rival does.
D. for each firm to advertise until the rival does not advertise, and then not advertise forever.
3. If you advertise and your rival advertises, you each will earn $4 million in profits. If neither of
you advertise, you will each earn $10 million in profits. However, if one of you advertises and
the other does not, the firm that advertises will earn $1 million and the non advertising firm will
earn $5 million. If you and your rival plan to be in business for only one year, the Nash
equilibrium is
A. For each firm to advertise.
B. For neither firm to advertise.
C. For your firm to advertise and the other not to advertise.
D. None of the statements associated with this question are correct.
Questions 4 &5 are based on this game, where firms one and two must independently decide
whether to charge high or low prices.
4.. Which of the following are the Nash equilibrium payoffs (each period) if the game is repeated
10 times?
A. (0, 0).
B. (5, -5).
C. (-5, 5).
D. (10, 10).
5.. Suppose the game is infinitely repeated. Then the "best" the firms could do in a Nash
equilibrium is to earn ___ per period.
A. (0, 0)
B. (5, -5)
C. (-5, 5)
D. (10, 10)
6. Consider the following entry game. Here, firm B is an existing firm in the market, and firm A
is a potential entrant. Firm A must decide whether to enter the market (play "enter") or stay out
of the market (play "not enter"). If firm A decides to enter the market, firm B must decide
whether to engage in a price war (play "hard"), or not (play "soft"). By playing "hard", firm B
ensures that firm A makes a loss of $1 million, but firm B only makes $1 million in profits. On
the other hand, if firm B plays "soft", the new entrant takes half of the market, and each firm
earns profits of $5 million. If firm A stays out, it earns zero while firm B earns $10 million.
Which of the following are Nash equilibrium strategies?
A. (enter, hard) and (not enter, hard).
B. (enter, soft) and (not enter, soft).
C. (not enter, hard) and (enter, soft).
D. (enter, hard) and (not enter, soft).
Answer questions 7-9 based on the following payoff matrix:
7. What are the secure strategies for Firm A and Firm B respectively?
A. (low price, high price).
B. (high price, low price).
C. (high price, high price).
D. (low price, low price).
8. Which of the following is true?
A. A dominant strategy for Firm A is "high price".
B. There does not exist a dominant strategy for Firm A.
C. A dominant strategy for Firm B is "low price".
D. none of the statements associated with this question are correct.
9. What are the Nash equilibrium strategies for Firm A and Firm B respectively in a one-shot
game?
A. (low price, low price).
B. (high price, high price).
C. (low price, high price).
D. (low price, low price) and (high price, high price).
10. Which of the following is true?
A. In a one-shot game, a collusive strategy always represents a Nash equilibrium.
B. A perfect equilibrium occurs when each player is doing the best he can regardless of what the
other player is doing.
C. Each Nash equilibrium is a perfect equilibrium.
D. Every perfect equilibrium is a Nash equilibrium.
11. Which of the following is true?
A. For a finitely repeated game, the game is played enough times to effectively punish cheaters
and therefore collusion is likely.
B. In an infinitely repeated game with a low interest rate, collusion is unlikely because the game
unravels so that effective punishment cannot be used during any time period.
C. A secure strategy is the optimal strategy for a player no matter what the opponent does.
D. None of the statements associated with this question are correct.
Refer to the following payoff matrix for questions12-14.
12. The dominant strategy for Player 2 is:
A. t1.
B. t1 and t2.
C. t3.
D. none of the statements associated with this question are correct.
13. The dominant strategy for Player 1 is:
A. S1.
B. S2.
C. S1 and S2.
D. none of the statements associated with this question are correct.
14. Which of the following strategies constitutes a Nash equilibrium of the game:
A. S1, t1.
B. S2, t2.
C. S2, t3.
D. S1, t2.
15. Which of the following conditions are necessary for the existence of a Nash equilibrium?
A. The existence of dominant strategies for both players.
B. The existence of a dominant strategy for one player and the existence of secure strategy for
another player.
C. The existence of secure strategy for both players.
D. none of the statements associated with this question are correct
Use the following information to answer question 16 -17:
Suppose that you are a manager. You are considering whether or not to monitor employees with
the payoffs in the following normal form game.
16. Which of the following pair of strategies constitute a Nash equilibrium?
A. Manager monitors and worker works.
B. Manager does not monitor and worker works.
C. Manager monitors and worker shirks.
D. None of the statements associated with this question are correct.
17. What should the manager do to solve the shirking problem?
A. Always monitor.
B. Never monitor.
C. Sincerely tell workers not to shirk.
D. Engage in "random" spot checks of the work place.
18. Management and a labor union are bargaining over how much of a $50 surplus to give to the
union. The $50 is divisible up to one cent. The players have one-shot to reach an agreement.
Management has the ability to announce what it wants first, and then the labor union can accept
or reject the offer. Both players get zero if the total amounts asked for exceed $50. Which of the
following is true?
A. There are multiple Nash equilibria.
B. ($25, $25) is a Nash equilibrium.
C. A Nash equilibrium is also a perfect equilibrium.
D. There are multiple Nash equilibria and ($25, $25) is a Nash equilibrium.
Refer to the following normal form game of price competition for questions 19-21.
19. Suppose the game is infinitely repeated, and the interest rate is 10%. Both firms agree to
charge a high price, provided no player has charged in low price in the past. If both firms stick to
this agreement, then the present value of Firm A's payoffs are:
A. 220.
B. 110.
C. 330.
D. 550.
20. Suppose that Firm A deviates from a trigger strategy to support a high price. What is the
present value of A's payoff from cheating?
A. 70.
B. 50.
C. 30.
D. 20.
21. What is the maximum interest rate that can sustain collusion?
A. 30%.
B. 15%.
C. 66.7%.
D. 20%.
22. It is easier to sustain tacit collusion in an infinitely repeated game if:
A. the present value of cheating is higher.
B. there are more players in the game.
C. the interest rate is lower.
D. the present value of cheating is higher and the interest rate is lower.
23. A coordination problem arises whenever there:
A. is no Nash equilibrium in a game.
B. is a unique Nash equilibrium but it is not very desirable.
C. are multiple Nash equilibria.
D. are no dominant strategies for both players.
There are two existing firms in the market for computer chips. Firm A knows how to reduce the
production costs for the chip and is considering whether to adopt the innovation or not.
Innovation incurs a fixed set-up cost of C, while increasing the revenue. However, once the new
technology is adopted, another firm, B, can adopt it with a smaller set-up cost of C/2. If A
innovates and B does not, A earns $20 in revenue while B earns $0. If A innovates and B does
likewise, both firms earn $15 in revenue. If neither firm innovates, both earn $5.
24. Under what condition will Firm B have an incentive to adopt if Firm A adopts the
innovation?
A. C > 30.
B. C < 30.
C. 10 > C > 0.
D. 35 > C > 25.
25. Under what condition will Firm A innovate?
A. C > 30.
B. C < 30.
C. 10 > C > 0.
D. 35 > C > 25.
Refer to the following normal form game of advertising for questions 26-.
26. Consider the above advertising game. Firms A and B know the game will be played for
exactly 5 periods. What is the Nash equilibrium to this game?
A. {Do Not Advertise, Do Not Advertise}.
B. {Advertise, Advertise}.
C. {Do Not Advertise, Do Not Advertise} provided the interest rate is less than 0.10 percent.
D. {Advertise, Advertise} provided the interest rate is less than 0.50 percent.
27. Suppose there is a 10 percent chance that the advertising game depicted in the above payoff
matrix will end next period. What is the present value to Firms A of agreeing to the strategy {Do
Not Advertise, Do Not Advertising}?
A. $125.
B. $237.50.
C. $1250.
D. None of the statements associated with this question are correct.
28. Suppose there is a 20 percent chance that the advertising game depicted in the above payoff
matrix will end next period. What is the present value to Firms B of cheating on the collusive
strategy {Do Not Advertise, Do Not Advertising}?
A. $0.
B. $10.
C. $125.
D. $175.
29. Suppose there is a 20 percent chance that the advertising game depicted in the above payoff
matrix will end next period. The collusive agreement {(Not Advertise, Not Advertise)} is
A. sustainable since $175 < $625.
B. unsustainable since $175 < $625.
C. sustainable since $10 > $50.
D. unsustainable since $10 > $50.
30. Suppose there is a 50 percent chance that the advertising game depicted in the above payoff
matrix will end next period. The collusive agreement {(Not Advertise, Not Advertise)} is
A. sustainable since $175 < $250.
B. unsustainable since $175 > $25.
C. sustainable since $20 > $50.
D. unsustainable since $350 > $50.
31. Suppose there is a 90 percent chance that the advertising game depicted in the above payoff
matrix will end next period. The collusive agreement {(Not Advertise, Not Advertise)} is
A. sustainable since $175 < $138.89.
B. unsustainable since $175 > $138.89.
C. sustainable since $11.11 < $50.
D. unsustainable since $11.11 > $50.