To identify a saddle point in a game matrix, we can apply the row minimum and column maximum method.

First, we will determine the minimum value in each row of the matrix. Consider the following example matrix:

In this matrix, the minimum values for each row are as follows:

• For row 1, the minimum is $2$.
• For row 2, the minimum is $1$.
• For row 3, the minimum is $1$.

Next, we will find the maximum value in each column of the matrix. In our example, the maximum values for the columns are:

• For column A, the maximum is $3$.
• For column B, the maximum is $5$.
• For column C, the maximum is $3$.

Now, we will search for any values in the matrix that are both a row minimum and a column maximum. In this case, the value $2$ located at cell $(2,1)$ is the only value that satisfies both conditions, making it the saddle point of the matrix.

If no value meets both criteria, then it can be concluded that the matrix lacks a saddle point.

In summary, to find a saddle point in a game matrix, one must first calculate the row minimums and column maximums, and then identify any values that fulfill both conditions.