Question 2 (Subgame-Perfect Nash Equilibrium Consider the following sequential game of imperfect information. 5,5 P2 (c) soning. T 0,6 P1 L P2 B ( 6,0 R 2,0 P2 I 1,1 PI b 0,2 e 5,1 P2 P2 A' R r 0,0 PI B' ( 0,0 P2 1,5 (a) How many information sets does this game have? What constitutes a strategy in a sequential game of imperfect information? (b) Find all the pure strategy subgame-perfect Nash equilibria of this game. Remember to write them down properly. Could this game support a SPNE in mixed strategies? Explain your rea- (d) Suppose this game were a game of perfect information. What would the game tree look like? What would be the SPNE outcome?
Question 2 (Subgame-Perfect Nash Equilibrium Consider the following sequential game of imperfect information. 5,5 P2 (c) soning. T 0,6 P1 L P2 B ( 6,0 R 2,0 P2 I 1,1 PI b 0,2 e 5,1 P2 P2 A' R r 0,0 PI B' ( 0,0 P2 1,5 (a) How many information sets does this game have? What constitutes a strategy in a sequential game of imperfect information? (b) Find all the pure strategy subgame-perfect Nash equilibria of this game. Remember to write them down properly. Could this game support a SPNE in mixed strategies? Explain your rea- (d) Suppose this game were a game of perfect information. What would the game tree look like? What would be the SPNE outcome?
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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Solve part C and D
Transcribed Image Text:Question 2 (Subgame-Perfect Nash Equilibrium
Consider the following sequential game of imperfect information.
5,5
P2
T
(c)
soning.
0,6
P1
P2
B
6,0
a
R
2,0
P2
1,1
5,1
0,2
P2
P2
A'
R
0,0
P1
B'
{
0,0
P2
(a)
How many information sets does this game have? What constitutes a
strategy in a sequential game of imperfect information?
(b)
Find all the pure strategy subgame-perfect Nash equilibria of this game.
Remember to write them down properly.
Could this game support a SPNE in mixed strategies? Explain your rea-
(d)
Suppose this game were a game of perfect information. What would the
game tree look like? What would be the SPNE outcome?
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