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.