For any given pay off matrix without saddle point the optimum mixed strategies are shown in Table
Mixed Strategies
Let p1 and p2 be the probability for Player A.
Let q1 and q2 be the probability for Player B.
Let the optimal strategy be SA for player A and SB for player B.
Then the optimal strategies are given in the following tables.
Optimum Strategies
p1and p2 are determined by using the formulae,
and p2= 1-p1
and q2= 1-q1
the value of the game w.r.t. player A is given by,
Example : Solve the pay-off given table matrix and determine the optimal strategies and the value of game.
Game Problem
Solution: Let the optimal strategies of SA and SB is as shown in tables.
Optimal Strategies
The given pay-off matrix is shown below in Table.
Pay-off Matrix or Maximin Procedure
Therefore, there is no saddle point and hence it has a mixed strategy. Applying the probability formula,
and p2= 1-p1
= 1-1/4= 3/4
and q2= 1-q1
=14/4
The optimum mixed strategies are shown in table below.
Optimum Mixed Strategies
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