Solved Solutions 4th ED.
Solutions to Chapter 2
Exercises SOLVED
EXERCISES
S1. (a) Assuming a sufficient supply of yogurt is available for all shoppers, each shopper is
simply making a decision. If some flavors of yogurt were in short supply, then it would be a game,
because shoppers could, for example, make sure to arrive at the store early in order to get their
preferred selections.
(b) Again, probably not an interaction between mutually aware players. (There may be
a strategic component to dress choice if the girls are aware that each is buying one and if there is
some benefit to being different from the others.)
(c) For a college senior, the choice here is a decision, unless you argue that a game is being
played with the student’s future self.
(d) This is a strategic interaction between mutually aware rival firms.
(e) The choice of running mate is a game played between different presidential candidates
looking forward to the payoffs of votes in an upcoming election.
S2. (a) (i) Simultaneous play; (ii) zero-sum; (iii) can be repeated, although description is of a
single play; (iv) symmetric imperfect information (neither player has information about the action being
taken by the other); (v) fixed rules; (vi) cooperative agreements are unlikely.
(b) (i) Sequential play; (ii) non-zero-sum game for voters; (iii) usually not repeated (though
some bills may face multiple votes); (iv) full information; (v) fixed rules; (vi) party apparatus may
provide mechanism for cooperation among members of the same party or even between parties.
(c) (i) Simultaneous play; (ii) non-zero-sum; (iii) not repeated; (iv) imperfect information;
(v) fixed rules; (vi) noncooperative.
S3. False. This statement rules out the possibility that individuals may be concerned about fairness.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
,Solved Solutions 4th ED.
S4. To solve each problem, the probability of each event must be multiplied by its respective payoff,
and then all the results must be added together for the expected payoff.
(a) Expected payoff = 0.5(20) + 0.1(50) + 0.4(0) = 15.
(b) Expected payoff = 0.5(50) + 0.5(0) = 25.
(c) Expected payoff = 0.8(0) + 0.1(50) + 0.1(20) = 7.
S5. Prediction is about looking into the future to foresee which actions and outcomes will arise,
whereas prescription is about giving advice regarding which actions should be taken. Prediction is
important for individuals outside a game who want to determine what will happen in it. Prescriptive
game theory can be used to help game players make good choices.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
,Solved Solutions 4th ED.
Solutions to Chapter 3
Exercises SOLVED
EXERCISES
S1. (a) There is one initial node (I) for Hansel making the first move; three decision nodes (D)
including the initial node, which represent the points where either Hansel or Gretel make a decision;
and six terminal nodes (T):
(b) There is one initial node (I) for Hansel making the first move; four decision nodes (D)
including the initial node, which represent the nodes where Hansel or Gretel make a decision; and nine
terminal nodes (T):
(c) There is one initial node (I) for Hansel making the first move; five decision nodes (D)
including the initial node, which represent the nodes where Hansel or Gretel make a decision; and eight
terminal nodes (T):
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
, Solved Solutions 4th ED.
S2. For this question, remember that actions with the same label, if taken at different nodes, are
different components of a strategy. To clarify the answers, the nodes on the trees are labeled 1, 2, and so
forth (in addition to showing the name of the player acting there). Actions in a strategy are designated as
N1 (meaning N at node 1), and so forth. The trees are below in the solutions to Exercise S3. Numbering
of nodes begins at the far left and proceeds to the right, with nodes equidistant to the right of the initial
node and numbered from top to bottom.
(a) Scarecrow has two strategies: (1) N or (2) S. Tinman has two strategies: (1) t
if Scarecrow plays N, or (2) b if Scarecrow plays N.
(b) Scarecrow has two actions at three different nodes, so Scarecrow has eight strategies: 2 • 2 • 2
= 8. To describe the strategies accurately, we must specify a player’s action at each decision node.
Scarecrow decides at nodes 1, 3, and 5, so we will label a strategy by listing the action and the node
number. For example, to describe Scarecrow choosing N at each node, we write (N1, N3, N5).
Accordingly, the eight strategies for Scarecrow are (N1, N3, N5), (N1, N3, S5), (N1, S3, N5), (S1, N3,
N5), (N1, S3, S5), (S1, N3, S5), (S1, S3, N5), and (S1, S3, S5).
Tinman has two actions at three different nodes, so Tinman also has eight strategies: 2 • 2 • 2 = 8.
Tinman’s strategies are (n2, n4, n6), (n2, n4, s6), (n2, s4, n6), (s2, n4, n6), (n2, s4, s6), (s2, n4, s6), (s2,
s4, n6), and (s2, s4, s6).
(c) Scarecrow has two actions at three decision nodes, so Scarecrow has eight strategies: 2 •
2 • 2 = 8. Scarecrow’s strategies are (N1, N4, N5), (N1, N4, S5), (N1, S4, N5), (S1, N4, N5), (N1, S4,
S5), (S1, N4, S5), (S1, S4, N5), and (S1, S4, S5). Tinman has two strategies: (t2) and (b2). Lion has two
strategies: (u2) and (d2).
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
Solutions to Chapter 2
Exercises SOLVED
EXERCISES
S1. (a) Assuming a sufficient supply of yogurt is available for all shoppers, each shopper is
simply making a decision. If some flavors of yogurt were in short supply, then it would be a game,
because shoppers could, for example, make sure to arrive at the store early in order to get their
preferred selections.
(b) Again, probably not an interaction between mutually aware players. (There may be
a strategic component to dress choice if the girls are aware that each is buying one and if there is
some benefit to being different from the others.)
(c) For a college senior, the choice here is a decision, unless you argue that a game is being
played with the student’s future self.
(d) This is a strategic interaction between mutually aware rival firms.
(e) The choice of running mate is a game played between different presidential candidates
looking forward to the payoffs of votes in an upcoming election.
S2. (a) (i) Simultaneous play; (ii) zero-sum; (iii) can be repeated, although description is of a
single play; (iv) symmetric imperfect information (neither player has information about the action being
taken by the other); (v) fixed rules; (vi) cooperative agreements are unlikely.
(b) (i) Sequential play; (ii) non-zero-sum game for voters; (iii) usually not repeated (though
some bills may face multiple votes); (iv) full information; (v) fixed rules; (vi) party apparatus may
provide mechanism for cooperation among members of the same party or even between parties.
(c) (i) Simultaneous play; (ii) non-zero-sum; (iii) not repeated; (iv) imperfect information;
(v) fixed rules; (vi) noncooperative.
S3. False. This statement rules out the possibility that individuals may be concerned about fairness.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
,Solved Solutions 4th ED.
S4. To solve each problem, the probability of each event must be multiplied by its respective payoff,
and then all the results must be added together for the expected payoff.
(a) Expected payoff = 0.5(20) + 0.1(50) + 0.4(0) = 15.
(b) Expected payoff = 0.5(50) + 0.5(0) = 25.
(c) Expected payoff = 0.8(0) + 0.1(50) + 0.1(20) = 7.
S5. Prediction is about looking into the future to foresee which actions and outcomes will arise,
whereas prescription is about giving advice regarding which actions should be taken. Prediction is
important for individuals outside a game who want to determine what will happen in it. Prescriptive
game theory can be used to help game players make good choices.
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
,Solved Solutions 4th ED.
Solutions to Chapter 3
Exercises SOLVED
EXERCISES
S1. (a) There is one initial node (I) for Hansel making the first move; three decision nodes (D)
including the initial node, which represent the points where either Hansel or Gretel make a decision;
and six terminal nodes (T):
(b) There is one initial node (I) for Hansel making the first move; four decision nodes (D)
including the initial node, which represent the nodes where Hansel or Gretel make a decision; and nine
terminal nodes (T):
(c) There is one initial node (I) for Hansel making the first move; five decision nodes (D)
including the initial node, which represent the nodes where Hansel or Gretel make a decision; and eight
terminal nodes (T):
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
, Solved Solutions 4th ED.
S2. For this question, remember that actions with the same label, if taken at different nodes, are
different components of a strategy. To clarify the answers, the nodes on the trees are labeled 1, 2, and so
forth (in addition to showing the name of the player acting there). Actions in a strategy are designated as
N1 (meaning N at node 1), and so forth. The trees are below in the solutions to Exercise S3. Numbering
of nodes begins at the far left and proceeds to the right, with nodes equidistant to the right of the initial
node and numbered from top to bottom.
(a) Scarecrow has two strategies: (1) N or (2) S. Tinman has two strategies: (1) t
if Scarecrow plays N, or (2) b if Scarecrow plays N.
(b) Scarecrow has two actions at three different nodes, so Scarecrow has eight strategies: 2 • 2 • 2
= 8. To describe the strategies accurately, we must specify a player’s action at each decision node.
Scarecrow decides at nodes 1, 3, and 5, so we will label a strategy by listing the action and the node
number. For example, to describe Scarecrow choosing N at each node, we write (N1, N3, N5).
Accordingly, the eight strategies for Scarecrow are (N1, N3, N5), (N1, N3, S5), (N1, S3, N5), (S1, N3,
N5), (N1, S3, S5), (S1, N3, S5), (S1, S3, N5), and (S1, S3, S5).
Tinman has two actions at three different nodes, so Tinman also has eight strategies: 2 • 2 • 2 = 8.
Tinman’s strategies are (n2, n4, n6), (n2, n4, s6), (n2, s4, n6), (s2, n4, n6), (n2, s4, s6), (s2, n4, s6), (s2,
s4, n6), and (s2, s4, s6).
(c) Scarecrow has two actions at three decision nodes, so Scarecrow has eight strategies: 2 •
2 • 2 = 8. Scarecrow’s strategies are (N1, N4, N5), (N1, N4, S5), (N1, S4, N5), (S1, N4, N5), (N1, S4,
S5), (S1, N4, S5), (S1, S4, N5), and (S1, S4, S5). Tinman has two strategies: (t2) and (b2). Lion has two
strategies: (u2) and (d2).
Games of Strategy, Fourth Edition Copyright © 2015 W. W. Norton & Company
