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1. Saddle point example ( Enter your problem )
 Method & Example-1Example-2 Other related methods

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### 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 B B1 B2 B3 B4 A1 20 15 12 35 A2 25 14 8 10 A3 40 2 10 5 A4 -5 4 11 0

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 RowMinimum 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 ColumnMaximum 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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