Prof.
Bryan Caplan
bcaplan@gmu.edu
http://www.bcaplan.com
Econ
812
HW
#3 (please type all answers)
1. Solve the following game using strict
dominance:
|
Player 2 |
|||
Player
1 |
|
Attack |
Defend |
Retreat |
Attack |
1,2 |
0,5 |
2,1 |
|
Defend |
2,0 |
6,3 |
3,2 |
|
Retreat |
3,4 |
1,5 |
4,3 |
2. Diagram the following game in extensive form,
then solve it using backwards induction.
a. Player 1 chooses left, center, or
right.
b. Player 2 chooses up, down, or
middle.
c. Player 1 chooses red, green, or
blue.
Payoffs
are as follows:
LUR |
2,3 |
CUR |
9,1 |
RUR |
1,1 |
LUG |
1,7 |
CUG |
8,6 |
RUG |
2,2 |
LUB |
5,4 |
CUB |
4,5 |
RUB |
3,3 |
LDR |
3,9 |
CDR |
0,2 |
RDR |
4,4 |
LDG |
9,1 |
CDG |
7,8 |
RDG |
5,5 |
LDB |
8,6 |
CDB |
5,4 |
RDB |
6,6 |
LMR |
4,5 |
CMR |
3,9 |
RMR |
7,7 |
LMG |
0,2 |
CMG |
2,3 |
RMG |
8,8 |
LMB |
7,8 |
CMB |
1,7 |
RMB |
9,9 |
3. Find the PSNE.
|
|
Player 2 |
|
Player 1 |
|
Left |
Right |
Up |
9,9 |
9,9 |
|
Down |
0,0 |
10,9 |
4. Find the MSNE for problem 3.
5. Re-diagram the extensive form of Entry game
if the Incumbent moves first instead of the Entrant. Does the subgame perfect equilibrium
change? Explain.
6. Re-diagram the extensive form of the
Coordination game if Player 1 moves first.
Does the set of equilibria (pure strategy and mixed strategy)
change? Why or why not?
7. Explain a simple, original, real-world
strategic situation of your choice. Draw
its extensive form and normal form. What
are the pure and mixed strategy Nash equilibria? (half
page)
8. Use game theory to analyze strategy in a
sporting event of your choice. Pay
particular attention to mixed strategy equilibria. (half
page)