Homework #7 Econ 612, Prof. Hanson
1. Find all pure strategy equilibrium of these normal-form games:
|
|
A |
B |
C |
|
A |
(0,0) |
(-1,2) |
(3,1) |
|
B |
(-1,2) |
(-3,5) |
(0,0) |
|
C |
(-2,0) |
(1,1) |
(-1,0) |
|
|
A |
B |
C |
|
A |
(3,-3) |
(1,1) |
(0,0) |
|
B |
(-1,-2) |
(0,0) |
(2,2) |
|
C |
(-3,5) |
(-2,1) |
(3,3) |
|
|
A |
B |
C |
|
A |
(1,1) |
(3,0) |
(5,0) |
|
B |
(0,3) |
(2,2) |
(9,2) |
|
C |
(0,5) |
(2,9) |
(4,4) |
2. Find all subgame perfect equilibria of these extensive form games:
|
First player picks |
|||
|
Second player picks |
Second player picks |
||
|
(1,2) |
(0,1) |
(1,3) |
(0,4) |
|
First player picks |
|||
|
Second player picks |
Second player picks |
||
|
(3,2) |
(0,1) |
(3,1) |
(2,2) |
|
First player picks |
|||
|
Second player picks |
Second player picks |
||
|
(9,0) |
(1,1) |
(4,4) |
(0,5) |
3. Bob and Joe are playing “chicken.” That is, they are driving toward each other at 40 miles an hour and they must each decide whether to stay on course or veer away. They will each lose 1000 if they crash. In addition they each care about their reputation for being tough. Bob gains 100 if he does not veer, while Joe gains 500 if he does not veer. Translate this situation into three game forms, one with simultaneous choice, one where Bob chooses first, and one where Joe chooses first. Fine the pure strategy subgame perfect equilibria of these games.