Game Theory
Homework 3
Find all pure strategy and mixed strategy Nash equilibria to the following games. Write
the equilibria in terms of p and q, where q is the probability that player 1 plays X and p is
the probability that player 2 plays A.
Game 1
Player 1
X
Y
Player 2
A
-1, -1
0, -5
p
B
-5, 0
-2, -2
(1-p)
q
(1-q)
What are the Nash equilibria?
Game 2
Player 1
X
Y
Player 2
A
5, 5
2, 0
p
B
0, 2
2, 2
(1-p)
q
(1-q)
What are the Nash equilibria?
Game 3
Player 1
X
Y
Player 2
A
0, 0
2, -2
p
B
-2, 2
-5, -5
(1-p)
What are the Nash equilibria?
q
(1-q)
Game 4
Player 1
X
Y
Player 2
A
5, 3
0, 0
p
B
1, 1
3, 5
(1-p)
q
(1-q)
What are the Nash equilibria?
Game 5
Player 1
X
Y
Player 2
A
3, -1
-1, 1
p
B
-1, 2
1, -1
(1-p)
What are the Nash equilibria?
q
(1-q)