I am trying to solve the problem for a 3-strategy dynamic system. But I get stuck from the beginning because I do not know how to deal with constants in the linear forms to matrix. I am not even sure I am doing it right with t-1 and t-2
The initial cost/reward matrix is like this: $$ \begin{array}{r|ccc} & 1:C & 2:D & 3:P \\ \hline 1:C & 1 & 0 & 1 \\ 2:D& k & 0 & 0 \\ 3:P & 1-j & -j & 1-j \end{array} $$
Which I proceed to write it down as:
$X_{c,t}+X_{d,t}+X_{p,t} = 1$
$X_t = X_{c,t}$
$X_{t-1} = 1 - X_{c,t}-X_{p,t}$
$X_{t-2} = 1 - X_{c,t}-X_{d,t}$
At this point, I do not know how to deal/translate those 1. I would end up with the coefficient matrix like this:
$$ \begin{pmatrix} 1 & 0 & 0 \\ -1 & 0 & -1 \\ -1 & -1 & 0 \\ \end{pmatrix}= \begin{pmatrix} X_t \\ X_{t-1}-1 \\ X_{t-2}-1\\ \end{pmatrix} $$
But then I do not know how to deal with $X_t-1$ and $X_{t-2}-1$ to solve this in order to derive the full dynamics. Hope it is clear, any help is appreciated.