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Operations Management - Game Theory, Goal Programming & Queuing Theory

Example of Graphical Solution Of A 2X2 Game With No Saddle Point

   Posted On :  25.06.2018 12:14 am

Consider the game with the following pay-off matrix.

Example of Graphical Solution Of A 2X2 Game With No Saddle Point
 
Consider the game with the following pay-off matrix.




We see that Maximum { row minima}  Minimum { column maxima }
 
So, the game has no saddle point. It is a mixed game.
 
Equations involving probability and expected value
 
Let p be the probability that player A will use his first strategy.
 
Then the probability that A will use his second strategy is 1-p.
 
Let E be the expected value of pay-off to player A.

When B uses his first strategy

The expected value of pay-off to player A is given by



When B uses his second strategy
 
The expected value of pay-off to player A is given by



Consider equations (1) and (2). For plotting the two equations on a graph sheet, get some points on them as follows:


Tags : Operations Management - Game Theory, Goal Programming & Queuing Theory
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