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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