Economics Homework Help

1 Problem 1

Consider the following static game:

L C R

T 3,1 0,0 5,0

M 2,1 1,2 3,1

B 1,2 0,1 4,4

1. Find all the pure strategy Nash Equilibria.

For parts 2-3, suppose this game is played for two periods. At the beginning of period 2, the

players can observe the outcome from period 1. There is no discounting.

2. Find all the pure strategy SPNE(s) for which the same pair of actions is played in period 2

regardless what happened in period 1.

3. Can the payo (4; 4) be achieved in period 1 in a pure strategy SPNE? If so, nd such a

SPNE; if not, prove why not.

2 Problem 2

Consider the following static Prisoner’s Dilemma game.

C D

C 2, 2 -3, 3

D 3, -3 0, 0

1. Are there any strictly dominated strategies? Find all the pure strategy Nash Equilibria.

For the following parts, suppose this game is played for innitely many times with discount

factor for both players 2 [0; 1).

2. Suppose = 0, nd all the SPNE(s).

3. Let both players adopt the following strategy: start with cooperation; cooperate as long as no

one has ever defected before; otherwise defect. Find the minimum value of such that this is

a SPNE.

4. For this part alone, suppose the payo matrix for the original static game has been changed

to:

C D

C 2, 1 -1, 4

D 3, -3 0, 0

How does your answer to part 3 change? Is the new minimum value of larger or smaller?

Explain.

5. Let both players adopt the following strategy: start with cooperation; cooperate if both players

cooperated or both players defected in the previous period; defect if one player defected and

another player cooperated in the previous period. In other words, the punishment for deviating

from cooperation only lasts for one period, and both players revert to cooperation immediately

after. Is it a SPNE if = 3=5? What if = 1=3?

6. Suppose = 1=4. Before the game starts, you tell the players that you will oer each of them

money m > 0 at each period both of them cooperate. At least how much should you oer to

make the strategy described in part 5 a SPNE?