How to find Mixed Nash Equilibrium and Correlated Equilibrium How do I find the mixed Nash equilibrium and Correlated Equilibrium of the following question? It looks impossible to find without any real numbers. 
Given that $ M>>1>>\epsilon $
\begin{pmatrix}
(M,M)& (1+\epsilon,1+\epsilon)&(2\epsilon,2\epsilon)&(\epsilon,\epsilon) \\
(1+\epsilon,1+\epsilon)&(1,1)&(\epsilon,\epsilon)&(0,0)\\
(2\epsilon,2\epsilon)&(\epsilon,\epsilon)&(M,M)&(1+\epsilon,1+\epsilon)\\
(\epsilon,\epsilon)& (0,0)&(1+\epsilon,1+\epsilon)&(1,1)
\end{pmatrix}
I tried to compute, but I failed to get a solution for the probabilities. 

Let $A$ be the payoff matrix you defined. Let $x = [x_1, x_2, x_3, x_4]^{\top}$. Let $y = Ax.$
The candidate to be a MNE is the vector $x$ such that:
$$y_1 = y_2 = y_3 = y_4.$$
By setting $x_4 = 1 -x_1-x_2-x_3$ and solving the previous system, one gets:
$$\begin{cases}
x_1 = \frac{\epsilon}{2\epsilon-M+1}\\
x_2 = \frac{1}{2}\frac{1-M}{2\epsilon-M+1}\\
x_3 = \frac{\epsilon}{2\epsilon-M+1}\\
\end{cases}.$$
In order for this vector to be a MNE, you should find out which are the values of $M$ and $\epsilon$ such that $x_1 \in (0,1)$, $x_2 \in (0,1)$ and $x_3 \in (0,1)$.
