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U4. (a) The strategic form of the game follows:
Severus = x Severus = y
Pure-strategy Nash equilibria are indicated by double borders. The unique subgame-perfect Nash
equilibrium is (SS, aa, y), with payoffs of (2, 1, 1).
(b) The equilibria (SN, aa, x), (SN, ab, x), and (SN, aa, y) cannot be subgame perfect because
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Minerva Minerva
aa ab ba bb aa ab ba bb
NN 1, 3, 1 1, 3, 1 4, 1, 4 4, 1, 4
NN 0, 2, 3 4, 1, 5 4, 1, 4 4, 1, 4
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
U5. (a) The payoff table is shown below. This game has a dominant strategy equilibrium: (Ads,
Ads).
Pepsi
Ads No ads
(b) See tree below. The subgame-perfect equilibrium is again (Ads, Ads); when both players
(c) This game is a prisoners’ dilemma. The (Ads, Ads) equilibrium is jointly inferior to the
U6. (a) The game table follows:
Vendor 2
A B C D E
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(b) Locations A and E are both dominated for both vendors.
175).
(d) In sequential play of the game, the vendor that moves first will choose either B or D and
U7. (a) The strategic form of this game follows:
Lion 3 = Eat Lion 2 Lion 3 = Not Eat Lion 2
Lion 2 Lion 2
Eat Lion
1
Not eat
Lion 1
Eat Lion
1
Not eat
Lion 1
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
In the equilibria (N, E, N) and (E, N, N), Lion 3 is making a noncredible promise not to eat Lion
U8. (a) The game tree is shown below:
(b) The subgame-perfect equilibrium of this game is (U, UU, RUUR) with payoffs of (5, 5,
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(c) The payoff table is shown below. Note that since Frieda appears as the row player and
Big Giant
Urban Rural
Titan Titan
Frieda’s UU UR RU RR UU UR RU RR
UUUU 1, 5, 5 1, 5, 5 5, 2, 5 5, 2, 5 5, 5, 2 3, 4, 4 5, 5, 2 3, 4, 4
UUUR 1, 5, 5 1, 5, 5 5, 2, 5 5, 2, 5 5, 5, 2 4, 4, 4 5, 5, 2 4, 4, 4
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
(d) There are 18 Nash equilibria in the table; the box with the double borders, (RUUR, UU,
U), is the subgame-perfect equilibrium in the sequential-play game. This equilibrium entails the same set
(c). Forcing Frieda’s to go third here does not change the store’s incentives in this matter, and we end up
U9. (a) Nancy’s best response to Monica’s choice m is
Monica knows Nancy’s best-response rule, so when she chooses her m to maximize her profit she can
plug in (1 + m/4) for n:
3/2.
(b) When m = 2 and n = 3/2 the profits are
In Exercise S10 of Chapter 5, when Monica and Nancy choose their effort levels simultaneously, their
profits are
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Both Monica and Nancy make higher profits when Monica commits to an effort level first, but Nancy
experiences a greater increase in her profits. This game thus has a second-mover advantage.
(c) Monica’s best response to Nancy’s choice n is
Nancy knows Monica’s best-response rule, so when she chooses her n to maximize her profit she can plug
Their payoffs are as follows:
As seen in part (b), both Monica and Nancy benefit when one commits to an effort level first, but the one
who moves second benefits more.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
