978-0393919684 Chapter 10 Solution Manual Part 1

Solutions to Chapter 10 Exercises

SOLVED EXERCISES

S1. False. The players are not assured that they will reach the cooperative outcome. Rollback

S2. (a) The payoffs are ranked as follows: high payoff from cheating (72) > cooperative payoff

(64) > defect payoff (57) > low payoff from cooperating (20). This conforms to the pattern in the text so

the game is a prisoners’ dilemma, as can also be seen in the payoff table given below:

Kid’s korner

High price Low price

If the game is played once, the Nash equilibrium strategies are (Low, Low) and payoffs are (57, 57).

(b) Total profits at the end of four years = 4  57 = 228. Firms know that the game ends in

(c) The one-time gain from defecting = 72 – 64 = 8. Loss in every future period = 64 – 57 =

(d) Total profits after four years = 4  64 = 256. With no known end of the world, the firms

(e) A 10% probability of bankruptcy translates into a 90% probability that the game

S3. (a) Payoffs are in thousands of dollars of salary. Each manager has a dominant strategy to

(b)

Managers still have a

(c) In this

version of the game, there

are two Nash equilibria at

S4. (a) The

Manager 2

Low effort High effort

Manager 2

Low effort High effort

Manager 2

Low effort High effort

(b) In the repeated version, honesty could be sustained by a “grim trigger strategy,” where if

your friend ever cheats you, you will never invest with him again. The friend can get an extra $120 = 130

(c) If the rate of interest is 10%, the above agreement cannot be sustained. Suppose an

alternative agreement is that your friend gets x and you get 130 – x. By cheating you once, he can get an

S5. (a) One manager is designated to choose High and the other Low. The High chooser makes a

(b) Defection entails refusing to make the side payment, so the cheater gets an extra 30 for

S6. In the k < 1 case, (Swerve, Swerve) maximizes the player’s joint payoff. Maintaining this type of

In this Chicken game, in contrast, if one driver succeeds in being the first to drive Straight (and

will continue to do so), it is not rational for the other driver to retaliate; if James is going Straight, Dean’s

In the k > 1 case, a pattern in which each player alternates between Swerve and Straight is, once

One difficulty that is likely to arise in this situation is in determining who gets the k payoff (and

who gets the –1 payoff) in the first round. With either discounting or an uncertain end to the game (or an

S7. (a) The joint profit of South Korea and Japan is

(b) When each country i produces half of the Q found in part (a), each will earn

(c) Assume that Korea decides to defect. (Because the per-unit costs are the same, the answer

will be identical if it is Japan that decides to defect.) Given that Japan is cooperating, Korea’s profit

funtion is

Japan’s profits will be

(d) Each year, Korea and Japan are playing following game (rounding to the nearest tenth

and assuming that when both defect each knows the other is also defecting, so that in that case they play

their Nash strategies):

Japan

Cooperate Defect