I have the following Payoff matrix:
$$\begin{pmatrix} 3&-5&0\\ 2&6&4\\ 2&5&6 \end{pmatrix}$$
I am trying to find an optimal strategy for both the row and the column players, but the method I familiar with only apply for 2x2 matrices. This specific matrix can't be reduced since there are no dominate rows or columns as far as I can see.
How to solve this payoff matrix and find the optimal strategies for the row and column players as well as the value of the game for this matrix ?
Note: One player is seeking to maximize and one to minimize, it's presented so -5 for example is the profit for the column player while it's the loss for the row player. Positive numbers are the profit of the row player. It's a zero sum game.
This following answer doesn't address my question since my matrix is not antisymmetric and have different criteria as far as I can tell : Finding the optimal mixed strategy of a 3x3 matrix game.
Can't you solve it by assigning variable probabilities to each of the first two rows and columns, calculating the expected payoff in terms of those variables, and then taking advantage of the fact that the first partial derivative of any of those variables must be $0$ (as otherwise one player would be able to improve his payoff by changing his probabilities) to get a linear system of four equations and four variables?