Find Solution of game theory problem using saddle point
| Player A\Player B | B1 | B2 | B3 |
| A1 | -2 | 14 | -2 |
| A2 | -5 | -6 | -4 |
| A3 | -6 | 20 | -8 |
Solution:
1. Saddle point testing
Players
| | | Player `B` | | |
| | | `B_1` | `B_2` | `B_3` | | |
| Player `A` | `A_1` | | -2 | 14 | -2 | |
| `A_2` | | -5 | -6 | -4 | |
| `A_3` | | -6 | 20 | -8 | |
We apply the maximin (minimax) principle to analyze the game.
| | | Player `B` | | |
| | | `B_1` | `B_2` | `B_3` | | Row
Minimum |
| Player `A` | `A_1` | | [(-2)] | 14 | -2 | | `[-2]` |
| `A_2` | | -5 | -6 | -4 | | `-6` |
| `A_3` | | -6 | 20 | -8 | | `-8` |
| Column
Maximum | | `(-2)` | `20` | `-2` | | |
Select minimum from the maximum of columns
Column MiniMax = (-2)
Select maximum from the minimum of rows
Row MaxiMin = [-2]
Here, Column MiniMax = Row MaxiMin = -2
`:.` This game has a saddle point and value of the game is -2
The optimal strategies for both players are
The player A will always adopt strategy 1
The player B will always adopt strategy 1
This material is intended as a summary. Use your textbook for detail explanation.
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