Exercise 4.8 Consider the extensive game Figure 4.22. (a) How many proper subgames does the game have? (b) How many of those proper subgames are minimal? b 2 3 03 g 0 1 h 20 Figure 4.22: The game of Exercise 4.8 Exercise 4.9 Find the Nash equilibria and the subgame-perfect equilibria of the game shown in Figure 4.23. 3 B E H 2 0 G 3 Figure 4.23: The game of Exercise 4.9 2 Exercise 4.11 Find the subgame-perfect equilibria of the game shown in Figure 4.25, assuming the following about the players' preferences. Both Amy and Bill are selfish and greedy, are interested in their own net gain, Amy values the object at $5 and Bill at $4. Amy $2 $3 Bill $3 $2 $3 Amy Amy Amy Pass $4 Pass $4 Pass $6 Pass $6 Bill Amy Bill wins wins wins Amy Amy wins wins Amy Bill wins wins Amy wins pays pays pays pays pays pays pays $4 $3 $4 $3 pays 56 $3 $6
Exercise 4.8 Consider the extensive game Figure 4.22. (a) How many proper subgames does the game have? (b) How many of those proper subgames are minimal? b 2 3 03 g 0 1 h 20 Figure 4.22: The game of Exercise 4.8 Exercise 4.9 Find the Nash equilibria and the subgame-perfect equilibria of the game shown in Figure 4.23. 3 B E H 2 0 G 3 Figure 4.23: The game of Exercise 4.9 2 Exercise 4.11 Find the subgame-perfect equilibria of the game shown in Figure 4.25, assuming the following about the players' preferences. Both Amy and Bill are selfish and greedy, are interested in their own net gain, Amy values the object at $5 and Bill at $4. Amy $2 $3 Bill $3 $2 $3 Amy Amy Amy Pass $4 Pass $4 Pass $6 Pass $6 Bill Amy Bill wins wins wins Amy Amy wins wins Amy Bill wins wins Amy wins pays pays pays pays pays pays pays $4 $3 $4 $3 pays 56 $3 $6
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Transcribed Image Text:Exercise 4.8 Consider the extensive game Figure 4.22.
(a) How many proper subgames does the game have?
(b) How many of those proper subgames are minimal?
b
2
3
03 g
0 1
h
20
Figure 4.22: The game of Exercise 4.8
Exercise 4.9 Find the Nash equilibria and the subgame-perfect equilibria of the game
shown in Figure 4.23.
3
B
E
H
2
0
G
3
Figure 4.23: The game of Exercise 4.9
2
Exercise 4.11 Find the subgame-perfect equilibria of the game shown in Figure 4.25,
assuming the following about the players' preferences. Both Amy and Bill are selfish
and greedy, are interested in their own net gain, Amy values the object at $5 and Bill at
$4.
Amy
$2
$3
Bill
$3
$2
$3
Amy
Amy
Amy
Pass
$4 Pass
$4 Pass
$6 Pass
$6
Bill
Amy Bill
wins
wins wins
Amy Amy
wins wins
Amy Bill
wins wins
Amy
wins
pays
pays pays
pays pays
pays pays
$4 $3
$4
$3
pays
56
$3
$6
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