Home > Operation Research calculators > Game Theory >> Saddle Point example

1. Saddle point example ( Enter your problem )
  1. Method & Example-1
  2. Example-2
Other related methods
  1. Saddle point
  2. Dominance method
  3. Algebraic method
  4. Calculus method
  5. Arithmetic method
  6. Matrix method
  7. 2Xn Games
  8. Graphical method
  9. Linear programming method
  10. Bimatrix method

2. Example-2
(Next example)

1. Method & Example-1



Method
saddle point Steps (Rule)
Step-1: 1. Select the minimum element from each row and write them in Row Minimum column.
2. Select the maximum element from Row Minimum column and enclose it in [ ]. It is called Row MaxiMin.
Step-2: 1. Select the maximum element from each column and write them in Column Maximum row.
2. Select the minimum element from Column Maximum row and enclose it in ( ). It is called Column MiniMax.
Step-3: 1. Find out the elements that is same in rectangle [ ] and circle ( ).
2. If Column MiniMax = Row MaxiMin then the game has saddle point and it is the value of the game.

Example-1
1. Find Solution of game theory problem using saddle point
Player A\Player BB1B2B3B4
A120151235
A22514810
A3402105
A4-54110


Solution:
1. Saddle point testing
Players
Player `B`
`B_1``B_2``B_3``B_4`
Player `A``A_1` 20  15  12  35 
`A_2` 25  14  8  10 
`A_3` 40  2  10  5 
`A_4` -5  4  11  0 


We apply the maximin (minimax) principle to analyze the game.

Player `B`
`B_1``B_2``B_3``B_4`Row
Minimum
Player `A``A_1` 20  15  [(12)]  35 `[12]`
`A_2` 25  14  8  10 `8`
`A_3` 40  2  10  5 `2`
`A_4` -5  4  11  0 `-5`
Column
Maximum
`40``15``(12)``35`


Select minimum from the maximum of columns
Column MiniMax = (12)

Select maximum from the minimum of rows
Row MaxiMin = [12]

Here, Column MiniMax = Row MaxiMin = 12
`:.` This game has a saddle point and value of the game is 12


The optimal strategies for both players are
The player A will always adopt strategy 1
The player B will always adopt strategy 3


This material is intended as a summary. Use your textbook for detail explanation.
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2. Example-2
(Next example)




 
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