978-0133020267 Chapter 11 Solution Manual

CHAPTER 11

GAME THEORY AND ASYMMETRIC INFORMATION

QUESTIONS

1. It is more of a problem for one-shot games.

2. It is a variable sum game.

3. It is more problematic for non-cooperative games.

4. It is easier for an irrational person to make a credible threat.

5. Because explicit bargaining is illegal.

6. Because firms need to agree on a joint outcome without being able to explicitly communicate with

7. Because if you can control the agenda you can create a tacit negotiation which has a solution that is

8. The bounds on the war need to be qualitative not quantitative. No price competition, not how much

9. Ace of spades.

10. A focal point.

11. Because different consumers will have different packets of information about the alternative

versions of a good and as a result will have different preferences over identical alternatives.

12. No, asymmetric information implies that there is imperfect information and one side has a

13. No.

14. Sellers have better information about the used cars they are selling than do buyers.

15. As price increases, average quality increases in the used car market. If the increase in demand due

16. The quality effect dominates.

17. When it is differentially costly to provide.

18. The job seeker has more information.

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19. Because it is differentially costly to obtain.

20. No, education acts purely as a signal within Spence’s model.

21. Yes because they are differentially costly to provide.

22. The buyer has more information in this instance.

23. Both act as a way of getting individuals to voluntarily separate themselves into groups according to

24. It is aimed at low risk individuals.

25. Yes, the Lemons model is an example of the adverse selection problem.

26. Profit sharing and stock options.

27. No because it is not differentially costly to provide.

PROBLEMS

1. a. Any dominant strategy equilibrium is also a Nash equilibrium. This is discussed in Tables 11.1

b. A game may have a Nash equilibrium even if it does not have a dominant strategy equilibrium.

c. Yes a firm can determine from the options available to the other firm that some strategies are

d. No, a dominant strategy equilibrium means that one strategy is dominant for each player.

2. a. People will shop for the week based on the days that the grocery stores are open. Some new

b.

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c. White’s dominant strategy is to open Sundays. Gray’s dominant strategy is to open Sundays.

d. Since this game is played repeatedly, each firm is likely to be able to signal via its actions that it

e. This is an example of a prisoners’ dilemma because the dominant strategy equilibrium is

3. a. The leader is Gray. Under all circumstances except when it is closed and White is open on

b. Gray does not have a dominant strategy. If White chooses to remain open then Gray should also

c. Gray should stay open on Sundays. By analyzing what White is likely to do the appropriate

d. No this is not a prisoners’ dilemma. Consider the closed/closed solution as the starting point

4. This is an example of a cooperative game. The fact that a better deal for you is certainly a worse

5. If negotiations cannot be explicitly agreed to (perhaps for legal reasons), then there is a greater need

6. a. 100% of cherry owners and 100% of lemon owners sell if P>$8,000. If P < $8,000, then no

b. Since buyers are risk neutral they are willing to pay a weighted average of the market clearing

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c. With s = 0.25, the weighted average price is $8,500 = 0.25·$4,000 + 0.75·$10,000. 25% of cars

d. With s = 0.5, the weighted average price is $7,000 = 0.5·$4,000 + 0.5·$10,000. 100% of cars

e. The weighted average price must be at least as large as the good used car owner’s reservation

f. We would have the same result but simply at a different value of s. In fact, we already know the

7. a. If all good cars are sold then all cars are sold so the fraction is 1. 1/3 are lemons.

b. If half of good used cars are sold then half are not. Since 1/3 of all cars are lemons, 2/3 are good

c. If one quarter of good used cars are sold then 3/4 are not. Since 1/3 of all cars are lemons, 2/3

d. The fraction sold is 1/3 + G·(2/3).

e. No, the weighted average price in this instance is $8,333 = 1/3·$5,000 + 2/3·$10,000. The

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f. Given the full information prices and fraction of lemons sold derived in D we have:

g. Inverse supply is a reservation price, PS(G). This can be set equal to PB(G) to obtain the market

8. To have a solution in which some good used cars are sold, we require that the reservation price for a

given level of G (the inverse supply equation) is at least as large as the weighted average price

derived in part (f).

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The price demanded by good used car owners in order to have half of them be offered for sale is

more than consumers would be willing to pay.

9. a. This is a constant elasticity demand function. The price elasticity of demand is -2 and the

b. A(0) = 0; A(5000) = 100/3 = 33.3; A(10000) = 50; A(15000) = 60; A(20000) = 66.6.

c. Average quality increases at a decreasing rate as price increases.

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g. This is most easily accomplished by programming A(P) and Q(P,A(P)) into Excel. The graphs

10. a. The firm should require 4 years of higher education. This is derived using Equation 21.4 that

relates wage offers with the cost of receiving the signal: (H – L)/CL < e < (H – L)/CH.

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b. Education is a signal in this instance because it is differentially costly to obtain.

c. In this model, there is no increase in productivity from education, per se. Educated workers are

11. a. Full coverage aimed at high risk individuals will pay out $4,000 with probability 0.3 so AFI

b. This pair of policies WILL screen individuals. Low risk individuals prefer coinsurance to full

high to no insurance:

High risk individuals prefer full high to coinsurance to no insurance:

Instructor’s note: A graph for Problem 11 was not requested, but if you wish to show students this