2, 1
0, 0
0, 0
1, 2
Opera
Movie
Opera
Movie
2
1
(O,O) is the best response for both players, so it is a Nash Equ
(O,M) is
not
the best response for both players, so it is
not
a Nash E
(M, O) is
not
the best response for both players, so it is
not
a Nash E
(M, M) is the best response for both players, so it is a Nash Equilib
M
L
K
J
Z
Y
X
5, 2
0, 4
3, 3
5, 6
3, 1
3, 7
7, 5
4, 4
3, 5
7, 5
8, 3
5, 6
2
1
This is a
strong
equilibrium since players would not want to move anywhere else
These are
weak
equilibriums since players would like to move to another equilibrium
2, 2
0, 3
3, 0
1, 1
Cooperate
Defect
Cooperate
Defect
2
1
Strict Nash Equilibrium
Nash Equilibriums
0, 0
3, 1
1, 3
2, 2
Hawk
Dove
Hawk
Dove
2
1
Strict Nash Equilibriums
2, 2
0, 0
0, 0
1, 1
A
B
A
B
2
1
There are no Nash Equilibriums!
1, -1
-1, 1
-1, 1
1, -1
Heads
Tails
Heads
Tails
2
1
This is firm 1’s best response equation
This is firm 2’s best response equation
1, -1
-1, 1
-1, 1
1, -1
Heads
Tails
Heads
Tails
2
1
There is a mixed strategy Nash where each player plays H or T 50% of the time.
1 - q
q
1, -1
-1, 1
-1, 1
1, -1
Heads
Tails
Heads
Tails
2
1
p
1 - p
B
C
F
by a combination of C and B. Likewise, F is also dominated by a mixed strategy for player 2. So what is this mixed strateg
B
C
F
2, 3
3, 2
3, 2
0, 5
5, 0
2, 3
2, 3
2, 3
0, 5
0, 5
3, 2
3, 2
2, 3
C
B
C
B
2
1
Payoffs:
Player 1:
0q + 3(1-q)
3q + 2(1-q)
Player 2:
5p + 2(1-p)
2p + 3(1-p)
Player 1 Plays:
(0, ¼, ¾)
Player 2 Plays:
(0, ¼, ¾)
S3
S2
S1
S1
6, -
2, -
1, -
2, -
5, -
4, -
7, -
2, -
3, -
S3
S2
at the other player will also choose a strategy that limits his losses.
Maxmin equilibrium (and also happens to be the Nash in this game)
3, 2
0, 4
6, 1
1, 3
X
Y
A
B
2
1
Nash
Equilibrium
There are no strictly dominated strategies in this game. Iterated dominance doesn’t help;
any belief that you may have about the other person is rational in this game.
But just because it’s rational doesn’t mean the belief is correct!
Nash Equilibrium: a strategy profile (strategy for each player) is a Nash equilibrium if and
only if each player’s strategy is a best response to the strategies of the other players.