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Solutions to Chapter 6 Exercises
SOLVED EXERCISES
S1. Second-mover advantage. In a sequential game of tennis, the second mover can best respond to
the first mover’s chosen action. Put another way, the second mover can exploit the information she learns
S2. The strategic form, with best responses underlined, is shown below:
Player 2
LL LR RL RR
There are two Nash equilibria: (D, LL) with payoffs of (3, 3) and (U, LR) with payoffs of (2, 4). Only the
S3. The strategic form is shown below:
Boeing
If In, then Peace If In, then War
There are two Nash equilibria: (In; If In, then Peace) and (Out; If In, then War). Only the first of these,
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
S4. (a) The strategic form follows:
Tinman
If N, then t If N, then b
(b) The only Nash equilibrium is (S; If N, then t) with payoffs of (1, 0).
S5. (a) The strategic form follows. The initials of the strategies indicate which action each player
would take at his first, second, and third nodes, respectively.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Tinman
nnn nns nsn nss snn sns ssn sss
NNN 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1
NNS 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1 0 , 1
Pure-strategy Nash equilibria are indicated by double borders. The unique subgame-perfect Nash
equilibrium is (SSN, nns), with payoffs of (4, 5).
(b) The remaining Nash equilibria are not subgame perfect because a player cannot credibly
threaten to make a move that will give himself a lower payoff than he would otherwise receive. The
S6. (a) The strategic form follows. The initials of the Scarecrow’s strategies indicate which
action he would take at his first, second, and third nodes, respectively.
Lion = u Lion = d
Tinman Tinman
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
t b t b
NNN 1, 1 , 1 2 , 3 , 2
NNN 1, 1 , 1 2 , 3 , 2
NNS 1, 1 , 1 2 , 3 , 2 NNS 1, 1 , 1 2 , 3 , 2
(b) Nash equilibria (SNS, t, u), (SNS, b, u), (SSS, t, u), and (SSS, b, u) are not subgame
S7. (a) The game tree is shown below:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
( b)
The rollback equilibrium for the game above is (Fast, Guess Fast/Guess Curve).
(c) The game tree is shown below:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
PITCHER
BATTER,
BATTER
PITCHER
PITCHER
0.30 , 0.70
0.15 , 0.85
0.20 , 0.80
0.35 , 0.65
It can also be represented as the tree in part (c) with an information set between the pitcher’s two nodes.
(e) The game table, with best responses underlined, follows:
Batter
Guess fast Guess curve
There is no cell where both players are mutually best responding. There is no Nash equilibrium in pure
strategies.
S8. (a) See table below. Best responses are underlined. There are 36 Nash equilibria shown by
shading in the cells of the table:
Emily
Contribute Don’t
Nina Nina
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Talia CC CD DC DD CC CD DC DD
1: CCCC 3, 3, 3 3, 3, 3 3, 4, 3 3, 4, 3 3, 3, 4 1, 2, 2 3, 3, 4 1, 2, 2
2: CCCD 3, 3, 3 3, 3, 3 3, 4, 3 3, 4, 3 3, 3, 4 2, 2, 2 3, 3, 4 2, 2, 2
3: CCDC 3, 3, 3 3, 3, 3 3, 4, 3 3, 4, 3 2, 1, 2 1, 2, 2 2, 1, 2 1, 2, 2
(b) Working with the normal form of the game, use iterated dominance of weakly dominated
strategies to find the subgame-perfect equilibrium. For Talia, strategy 1 is weakly dominated by strategy
The set of strategies that leads to the subgame-perfect equilibrium is the only set in which all
three women use strategies that entail choosing “rationally” (that is, choosing the action that leads to the
S9. The larger tree follows:
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
