Difference between revisions of "Pure strategy game"
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| − | + | The so called ''Maximin'' strategy aims to to select the maximum value of the minimum of the rows: | |
| + | {| class="wikitable" | ||
| + | ! | ||
| + | ! | ||
| + | !B1 | ||
| + | !B2 | ||
| + | !Row minimum | ||
| + | |- | ||
| + | |Game player A | ||
| + | |A1 | ||
| + | |3 | ||
| + | |4 | ||
| + | |'''3''' | ||
| + | |- | ||
| + | | | ||
| + | |A2 | ||
| + | |1 | ||
| + | |-2 | ||
| + | |-2 | ||
| + | |- | ||
| + | |}With the maximin strategy on the above example '3' is the maximum value of the two minimums of the row. | ||
| + | |||
| + | The so called ''Minimax'' strategy aims to to select the minium value of the maximum of the columns (the largest loss) | ||
| + | {| class="wikitable" | ||
| + | ! | ||
| + | ! | ||
| + | !B1 | ||
| + | !B2 | ||
| + | !Row minimum | ||
| + | |- | ||
| + | |Game player A | ||
| + | |A1 | ||
| + | |3 | ||
| + | |4 | ||
| + | |3 | ||
| + | |- | ||
| + | | | ||
| + | |A2 | ||
| + | |1 | ||
| + | |-2 | ||
| + | |-2 | ||
| + | |- | ||
| + | | | ||
| + | | | ||
| + | |'''3''' | ||
| + | |4 | ||
| + | | | ||
| + | |- | ||
| + | |}With the maximin strategy on the above example '3' is the minimum value of the two maximum values of the column. | ||
| + | |||
| + | The value of '3' is the maximum of player A's minimum gains. It is also the minimum of player B's maximum losses. If this point it is called a ''saddle point'' and it will mean that each player will play the same strategy each time. It is therefore called a ''pure strategy game'' | ||
| + | |||
| + | Part of [[M7-Quantitative Decision Methods-S5 - Game Theory|M7-Quantitative Decision Methods-S5 - Game Theory]] | ||
[[Category:mbi]] | [[Category:mbi]] | ||
Latest revision as of 20:02, 27 August 2020
The so called Maximin strategy aims to to select the maximum value of the minimum of the rows:
| B1 | B2 | Row minimum | ||
|---|---|---|---|---|
| Game player A | A1 | 3 | 4 | 3 |
| A2 | 1 |
With the maximin strategy on the above example '3' is the maximum value of the two minimums of the row.
The so called Minimax strategy aims to to select the minium value of the maximum of the columns (the largest loss)
| B1 | B2 | Row minimum | ||
|---|---|---|---|---|
| Game player A | A1 | 3 | 4 | 3 |
| A2 | 1 | |||
| 3 | 4 |
With the maximin strategy on the above example '3' is the minimum value of the two maximum values of the column.
The value of '3' is the maximum of player A's minimum gains. It is also the minimum of player B's maximum losses. If this point it is called a saddle point and it will mean that each player will play the same strategy each time. It is therefore called a pure strategy game