Math 486 Game Theory Miderm 2 March 20, 2003. 5 problems,
13 pts each.
Name
1-3. Solve matrix games:
1.
| 1 |
3 |
5 |
7 |
1 |
3 |
2 |
| 7 |
8 |
6 |
8 |
7 |
6 |
6 |
| 1 |
-5 |
4 |
3 |
4 |
0 |
1 |
| 3 |
5 |
6 |
-3 |
0 |
1 |
3 |
| 2 |
3 |
-2 |
0 |
1 |
2 |
0 |
2.
| 0 |
0 |
0 |
-2 |
-2 |
-1 |
-2 |
| 0 |
4 |
3 |
-1 |
-2 |
-1 |
-1 |
| 0 |
4 |
3 |
0 |
-2 |
0 |
-1 |
| 3 |
0 |
-3 |
0 |
2 |
2 |
0 |
| 0 |
3 |
3 |
-2 |
-3 |
0 |
0 |
3.
| 0 |
1 |
-1 |
1 |
| -1 |
0 |
1 |
1 |
| 1 |
-1 |
0 |
1 |
4-5. Solve the linear programs, where all xi
>= 0:
4.
| x1 |
x2 |
x3 |
x4 |
x5 |
1 |
|
| 1 |
2 |
-3 |
5 |
6 |
-2 |
= -x6 |
| 0 |
-1 |
2 |
0 |
3 |
1 |
= x7 |
| -1 |
0 |
2 |
4 |
-4 |
2 |
= x8 |
| 2 |
0 |
3 |
0 |
1 |
2 |
= f -> min |
5.
| x1 |
x2 |
x3 |
x3 |
x5 |
-1 |
|
| 1 |
2 |
-3 |
5 |
6 |
-2 |
= -x6 |
| 0 |
-1 |
2 |
0 |
3 |
1 |
= x7 |
| -1 |
0 |
2 |
4 |
-4 |
2 |
= 0 |
| 2 |
0 |
3 |
0 |
1 |
2 |
-> max |