eco 444 test 3

Test 3

ECO 444

Konrad Grabiszewski

• This is an individual take-home test. Prepare the answers on your own.

• Deadline: deliver your answers in class on Monday, April 9, 2018.

• To deliver: only the last page (detach and sign).

Exercise 1 (70 points)

For each tree, find all pure strategy Nash equilibria (NE), and all pure strategy subgame-perfect

Nash equilibria (SPNE). In every tree, payoffs are in alphabetical order. You can gain up to 10

points per tree (5 points for NE, 5 points for SPNE).

Ann

Bob

C

3,0 2,2

D

A B

1,1

Tree 1

Ann

Bob

C

1,0 2,2

D

A B

Bob

E

2,0 1,1

F

Tree 2

Ann

Bob

C

1,1 1,1

D

A B

Bob

E

1,1 1,1

F

Tree 3

Ann

Bob

C

1,0 0,1

D

A B

C

0,1 1,0

D

Tree 4

1

Ann

Bob

D

3,3 0,0

E

A C

Bob

F

3,3 4,4

G F

5,5 1,1

G

B

Tree 5

Ann

Bob

D

3,3 0,0

E

A C

D

3,3 4,4

E D

5,5 1,1

E

B

Tree 6

Ann

Bob

D

3,3 0,0

E

A C

Bob

F

3,3 4,4

G D

5,5 1,1

E

B

Tree 7

Exercise 2 (30 points)

For each tree, find all pure strategy subgame-perfect Nash equilibria (SPNE). In every tree, payoffs

are in alphabetical order. You can gain up to 10 points per tree.

Ann

L

7,0

R

Bob

T

8,4

B

Ann

P

9,2 1,4

S

Tree 1

2

Ann

Bob

A

0,0 3,5

B

Z

C

1,1 5,3

D

X

Bob Bob

E

3,5 0,0

F G

6,3 1,1

H

Bob

Y T

Tree 2

Ann

Bob

C

1,0,1,6

D

A B

G

0,2,5,4 0,4,1,3

H

Chris

E

4,5,6,0

F

Bob

K

3,5,0,8 1,2,2,9

L

David

Tree 3

3

Test 3

ECO 444

Konrad Grabiszewski

Name: _______________________________________________________________________________

Exercise 1

tree NE SPNE

1

2

3

4

5

6

7

Exercise 2

tree SPNE

1

2

3