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Solutions to Chapter 4 Exercises
UNSOLVED EXERCISES
U1. (a) For Colin, Right dominates Left, so Left is eliminated. Then for Rowena Up dominates
(b) Starting with Colin, Left dominates Right, so Right is eliminated. Then for Rowena
(c) Beginning with Rowena, Straight dominates Up, so Up is eliminated. Then for Colin,
(d) The game is solved using iterated dominance. Colin has no dominated strategies. For
U2. (a) Not zero-sum. Payoffs sum to different totals in each cell.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
U3. (a) Not zero-sum so minimax is not applicable.
Rowena chooses the maximum of 3, which comes from playing Straight. The minima of Colin’s strategies
(d) The minima of Rowena’s strategies are 5 for Up, 3 for High, 2 for Low, and 3 for Down,
U4. (a) Left dominates Right for Colin, so Right is eliminated. With only Left, Down dominates
(b) Neither player has any dominant strategies; best-response analysis shows that there are
(c) Down is a dominant strategy for Rowena, so Up may be eliminated. Then for Colin Right
(d) Up dominates Straight for Rowena, so Straight is eliminated, but afterward, there are no
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
U5. Beginning with Colin, Middle dominates Right (remember that –2 < –1), so Right is eliminated,
U6. Beginning with Colin, Left dominates Center, so Center is eliminated. Then for Rowena, Level
U7. (a) Colin’s payoffs against Bottom are complete, so they indicate that Center should be the
(b) As seen in part (a), Colin will not have a dominant strategy if either his payoff from
(Middle, Center) is less than 5 or his payoff from (Top, Left) is greater than 2. Similarly, Rowena will not
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Colin
Left Center Right
U8. (a) The payoff table follows:
Japanese Navy
North South
Air Force
(b) The Japanese Navy has a weakly dominant strategy to go North. The Americans will also
U9. (a) The payoff table follows:
Jill
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
G K L Q R W
G3, 6 0, 0 0, 0 0, 0 0, 0 0, 0
There are six pure-strategy Nash equilibria, each of which entails the two players choosing the
(b) Any equilibrium could be focal, depending on the underlying common cultural
understandings of the two players; to achieve a focal equilibrium, their expectations must converge. In a
U10. (a) The game tables follow:
Larissa Black Kristin
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Black Lavender Yellow
Larissa Lavender Kristin
Black Lavender Yellow
Larissa Yellow Kristin
Black Lavender Yellow
(b) There are no dominated strategies. No player always does best choosing one color.
(c) There are six pure-strategy Nash equilibria: (Yellow, Lavender, Black), (Lavender,
U11. (a) The strategic form of the game follows:
David B
Colleen
B N
David N Colleen
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
B N
(b) There are no dominant strategies, so we must use best-response analysis, which reveals
(c) There are no focal points distinguishable by payments, but there may be a focal point
based upon the gender of the purchaser or customs of social occasions. In a society where men are
U12. (a) The normal form follows:
Ted 1
Sara
1 2
Ted 2
Sara
1 2
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(b) By best-response analysis, we see that there are two pure-strategy Nash equilibria. One
U13. Below is one example of a payoff table that meets the requirements. There are infinitely many
that do so (and infinitely many that do not):
Colin
Left Straight Right
1. Each player has three strategies.
2. Neither side has a dominant strategy.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
