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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
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(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
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
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
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
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
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(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
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
