Solving Two-Person and Zero-Sum Game

Two-person zero-sum games can be probabilistic or deterministic. The deterministic games will owe saddle points and pure strategies lies in such games. On the contrary, the probabilistic games will not have any saddle points and mixed strategies are taken with the aid of probabilities.

Definition of saddle point

A saddle point of a matrix is the position of an element in payoff matrix, which is least in its row and the maximum in its column.

Process to determine the saddle point

• Choose the minimum element of every row of the payoff matrix and mark them through circles.
• Choose the maximum element of every column of the payoff matrix and mark them by squares.
• If seems there an element in the payoff matrix with a circle and a square jointly then that position is known as saddle point and the element is the value of the game.

Solution of games with saddle point

To get a solution of a game with a saddle point, it is possible to determine

• Top strategy for player A
• Top strategy for player B
• The value of the game

The optimum strategies for player A and B will be those which match up to the row and column respectively with the saddle point.