The LHS is the payo matrix for the case in which Firm 1 is H-type and RHS is the one for
the case in which Firm 1 is L-type. Assume that Firm 2 believes that Firm 1 is H-type with
3
probability 4 : Derive the Bayesian Nash equilibrium when both rms make d

2. (20 points)
Consider the following game.
1) (5p) Derive every pure strategy Nash equilibrium.
2) (5p) From your answer of 1), Without doing any mathematical analysis, you should know that there exists
a mixed strategy equilibrium. Explain Why.
3) (10

2. (15 points)
Three rms (rm 1, rm 2, and rm 3) are competing in one market where the market demand function is
P = 10 Q. Each rm cost function is T C = 0. In period 1, rm 1 decides q1 as the leader. Then, in period 2,
s
rm 2 and rm 3 decide their output

3) Derive the subgame perfect Nash equilibrium.
3. Consider the following game. Assume G(T < 1):
L
R
U
1; 1 4; 0
D
0; 4 3; 3
Derive the subgame perfect Nash equilibrium.
4. Consider the following game. Assume G(T = 2):
L
R
U
2; 1 2; 0
D
1; 2 4; 3
1) Deriv

Here, the rst term is the slope and the second term is Y-intercept.
Example
Find the linear function that passes through following two points. A = (2, 4) and B = (4, 2)
2.2
When f (x) = ax2 + bx + c
Suppose that the function is given as follows.
y = f (x)

So, we have an unique equilibrium and it is a mixed Nash equilibrium. Finally,
2 3
2. (10 point) Consider the following normal form game.
1) (5p) Is this game solvable using IESDS?
2) (5p) Derive every Nash Equilibrium.
Solution)
1)
Yes. This game is

Player 1
L
R
Player 2
B
A
3
1
D
C
1
2
2
1
0
0
1) Check how many subgames are in this extensive form game.
2) Draw the payo matrix of the strategic form game equivalent to the above extensive form
game.
3) Find the pure strategy Nash equilibrium.
4) Find t

4) Check whether the derived answer in 3) is the ecient outcome or not.
4. Bush and Clinton plan to meet at the cinema. However, they forget to decide whether to
meet for the morning show (M) or the night show (N). Each must choose independently between
M

So,
Le = 2
Then,
L = 1 6= Le = 2
So, the labor demand L in a subgame perfect Nash equilibrium is not an e cient outcome.
2
2. (20 points)
Consider the following stage game. Suppose G(T = 2) and x > 5. Assume that the payos of T = 2 are not
discounted, i.e

Handout 2 The Bertrand Model with Product
Differentiation
In the Bertrand model it is assumed that each firm sets price to maximise profits. In
what follows we provide a simple example of the case where products are
differentiated.
Assume that there are t

Chapter 4 Sequential Games
1
Extensive Form Games
T
H
H
(1,2)
Anyfinitegameofperfect
informationhasapurestrategy
Nashequilibrium.Itcanbefound
bybackwardinduction.
T
(2,1)
T
H
(2,1)
(4,0)
Chessisafinitegameofperfectinformation.Thereforeitisa
trivialgamefro

Handout 1 The Cournot Model
In the Cournot model it is assumed that each firm sets output to maximise profits. As an
example, assume that there are two firms in the market, 1 and 2. The market demand
curve is p = 150 2Q where p is market price and Q is ma