CIT 591 Game Theory Examples
Fall 2010, David Matuszek

To test your Mixed Strategy program, you need some games for which you know the correct answers. Unless you are a game theorist, I need to supply them. So here are a few:

4
-3
-5
12
Best strategy for Max: [0.708, 0.291]
Best strategy for Min: [0.624, 0.375]
2
5
5
2
Best strategy for Max: [0.5, 0.5]
Best strategy for Min: [0.5, 0.5]
-2
3
3
-4
Best strategy for Max: [0.583, 0.417]
Best strategy for Min: [0.583, 0.417]
2
4
6
0
Best strategy for Max: [0.75, 0.25]
Best strategy for Min: [0.5, 0.5]
10
20
35
5
Best strategy for Max: [0.75, 0.25]
Best strategy for Min: [0.375, 0.625]
2
7
6
9
5
1
4
3
8
Best strategy for Max: [0.333, 0.333, 0.332]
Best strategy for Min: [0.333, 0.333, 0.333]
-9
12
-6
7
14
5
10
-8
3
6
17
-10
This array has a saddle point at row 1, column 2

Strategies do not need to be computed for a game with a saddle point; but if you computed them anyway, you should get:
Best strategy for Max: [0.0, 1.0, 0.0, 0.0]
Best strategy for Min: [0.0, 0.0, 1.0]
1
2
3
3
2
1

Best strategy for Max: [0.5, 0.5]
Best strategy for Min: [0.5, 0.0, 0.5]

1
3
2
2
3
1
Best strategy for Max: [0.5, 0.0, 0.5]
Best strategy for Min: [0.5, 0.5]
-5
0
5
0
10
-10
2
-2
0
Best strategy for Max: [0.25, 0.125, 0.625]
Best strategy for Min: [0.333, 0.333, 0.333]
-2
-1
0
0
1
2
1
2
-3
-3
2
1
-1
2
0
0
-2
-1
0
3
2
2
1
-2

Best strategy for Max: [0.221, 0.333, 0.0, 0.444]
Best strategy for Min: [0.389, 0.0, 0.277, 0.0, 0.0, 0.333]

This is not a good array to use for JUnit testing, because columns 2 and 3 are identical. You don't care which column the program chooses, so you shouldn't test which one it chooses.

On the other hand, you could make a useful test out of this game by eliminating one of those columns.