To identify the saddle point and value of game the following procedure to be adopted on

the payoff matrix :

(i) Identify the minimum from each row and place a symbol * in that cell/entry. Take the maximum of these minima.

(ii) Identify the maximum from each column and place a symbol x in that cell/entry. Take the minimum of these maxima.

(iii) If both the symbols * and x occurs in a/an cell/entry, then that cell/entry is called saddle point and the value in that cell/entry is called value of the game (v).

Also v = Maximum (row minima) = Minimum (column maxima). There may be more than one saddle point but the value of the game is unique

**Example 1** . Solve the following game :

Player B

A1 | 1 | 5 | 4 | 2 | |||

PLAYER A | A2 | 2 | 3 | 5 | 3 | ||

A3 | 3 | 4 | 5 | 3 |

**Solution.** The calculations are displayed in the following table :

Player B

B 1
A1 1* Player A A2 2* A3 3*X Max. 3 |
B2 B3
5x 4 3 5x 4 5x 5 5 |
B4 Min.
2 1 3x 2 3*x 3 3 |

Max. (Row Min.) = 3,

Min. (Column Max.) = 3

In the above game, there are two saddle points at (A3, B1) and (A3, B4).

The value of the game is 3. Here the optimal strategy for player A is A3 and the optimal strategy for player B is B 1 and B4.

**Example 2.** Determine the solution of the following game :

**Solution.** In the given game, player A has 4 strategies and player B has 5 strategies. The calculations are displayed in the following table :

Max. (Row Min.) = 4, Min. (Col Max.) = 4

In this game there is one saddle point at (A2, B2)

The value of the game is 4.

The optimal strategy for player A is A2

and the optimal strategy for player· B is B2.