Unit 8: Game Theory
Note
In this unit, you will either have a problem on maximin or minimax principle for 5 marks. They are
extremely easy and can be learnt by following the simple steps below.
Maximin and Minimax Principle
In this Player A wants to maximize his gain while Player B wants to minimize his loss
The following steps are involved:
1. Identify the minimum gain corresponding to each strategy of A. Write the row minimum on right
of each row. Find out the maximum of these, this is known as maximin.
2. Identify the maximum loss corresponding to each strategy of B. Write the column maximum at
the bottom of each column. Find out the minimum among these, this is known as minimax.
If the maximin and minimax are equal, the game is said to have a saddle point. Let the position of the
saddle point in the pay-off matrix be (r, s) then the suggested pure strategy for Player A is A r and
suggested pure strategy for Player B is Bs .
The pay off at the position of the saddle point is called value of the game.
Dominance Principle
1. If all the elements of a row in the payoff matrix say kth rpw are greater than or equal to the
corresponding elements of another row in the payoff matrix say rth row then the kth row
dominates rth row. Thus the rth row of the payoff matrix can be deleted.
2. If all the elements of a column in the payoff matrix say pth column are lesser than or equal to the
corresponding elements of another row in the payoff matrix say qth row then the pth row
dominates qth row. Thus the qth row of the payoff matrix can be deleted.
3. This process can be deleted until the optimal strategy is obtained.