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

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

 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 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.
Any bug, improvement, feedback then Submit Here

 2. Example-2 (Next example)

Dear user,

We've detected that you are using AdBlock Plus or some other adblocking software which is preventing the page from fully loading.

We don't have any banner, Flash, animation, obnoxious sound, or popup ad. We do not implement these annoying types of ads!