# Homework#6: Game theory ```Homework #6. Game Theory (10pts)
1. Find all pure strategy Nash equilibria in the following game, or show that none exist
a. Draw arrows representing each player’s choices
b. Show equilibrium (or equilibria)
Player 2
A
B
A
3, 2
2, 1
B
2, 1
4, 2
Player 1
2. For which values of X (if such X exists) the following game does not have a pure strategy
equilibrium, or show that this game always has one (or more) Nash equilibria
Player 2
A
B
A
4,10
1, 12
B
X, 14
2, 2
Player 1
3. Cost of two firms is given by C  Q   Q , market demand is given by Q  25  P . Firm 1 can
credibly commit to a quantity choice before firm 2 makes its choice.
a. Fill out the rest of the payoffs
b. Find all pure strategy subgame perfect Nash equilibria in the following game
QFollower=6
___, ___
Firm 2
QCournot=8
___, ___
QFollower=6
___, ___
QCournot=8
___, ___
Firm 1
QCournot=8
Firm 2
4. Starting with the setup of the previous problem now assume that there is a fixed cost of 30 in the
production function and the leader can attempt to prevent entry by limit pricing.
a. Fill out the payoff matrix
b. Find all pure strategy subgame perfect Nash equilibria in the following game
Enter, QFollower=6
___, ___
Firm 2
Not enter, Q=0
_____, 0
Enter, Q=__
____,_____
Not enter, Q=0
______, 0
Firm 1
QLimit=14
Firm 2
5. Solve problem 3 at the end of chapter 6
6. Solve problem 4 at the end of chapter 6. This problem is optional but a good attempt is required.
This problem demonstrates how the nature of the competition affects how firms react to changes
in prices. You may use formulas from the appendix to find the answer.
7. Solve problem 7 at the end of chapter 6
```