# Political Science

POSC015: Comparative Politics Problem Set I

1. (45 pts.) Solve problems 3 (10 pts), 9 (only last four statements, 10 pts), 11 (only the statement about the senators, 10 pts), and 13 (15 pts) in Chapter 2 of Clark, et al.

2. (40 pts.) Solve problems 2 (15 pts) & 4 (25 pts) in Chapter 3 of Clark, et al.

3. (10 pts.) Consider the extensive form game below.

(a) What are the strategies of each of the three players?

(b) What are the subgame perfect equilibria of the game?

P1

P2

(3,4,1)

C

(1,3,3)

D

(1,2,1)

E

A

P2

(6,1,1)

F

P3

(6,0,1)

I

(2,2,2)

H

G

B

Indridi H. Indridason Fall 2020

POSC015: Comparative Politics Problem Set I

4. (10 pts) Consider the extensive form game below.

(a) What are the subgame perfect equilibria of the game?

P1

P2

(3,4,1)

C

(1,3,3)

D

(1,2,1)

E

A

P2

(6,2,1)

F

P3

(6,0,1) I

(2,3,2)

H

G B

5. (15 pts.) Find the Nash equilibria of the games. [Note on best replies: If the best reply is not unique then all the actions that result in the highest payo� are best replies.]

(a) .

Candidate 2 L R

Candidate 1 U 0, 0 1, 1 D 1, 1 0, 0

(b) .

Candidate 2 L R

Candidate 1 U 0, 0 100, 100 D 1, 1 0, 0

Indridi H. Indridason Fall 2020

POSC015: Comparative Politics Problem Set I

(c) .

Candidate 2 L R

Candidate 1 U 1, 1 1, 1 D 1, 1 1, 1

6. (5 pts.) Watch these two clips from the British game show `Golden Balls’: Clip 1 and Clip 2. Draw the strategic form game of the second clip (the structure of the game in the two clips is identical only the money at stake di�ers). Does the game resemble any game that you are familiar with? The way the game is played in the second clip is a little may seem a little surprising? Consider the game you have just drawn can you make sense of why the players adopted their strategies?

7. (5 pts.) Can you think of a political situation that resembles the prisoner’s dilemma (the state of nature game)? That is, a situation where, e.g., both (all) actors have an incentive to choose a particular action when the actors would have been better o� not choosing that action. Brie�y explain why (bonus for sketching the game)

Make sure you explain how you arrive at your solution � you won’t receive partial credit for incorrect answers unless we can see that you have done a part of the problem correctly. It is your responsibility to convey the answers in a clear manner. The homework is due at the beginning of class on October 22.

Indridi H. Indridason Fall 2020

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