[Tex/LaTex] Game theory: payoff matrix with arrows

Question

Based on strategy / payoff matrix I would like to add arrows to indicate equilibria; in such a way that this

becomes like this

Any suggestion would be greatly appreciated.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{calc}
\usetikzlibrary{matrix}
\usetikzlibrary{positioning}

\begin{document}

\begin{tikzpicture}

\matrix[matrix of math nodes,every odd row/.style={align=right},every even row/.style={align=left},every node/.style={text width=1.5cm},row sep=0.2cm,column sep=0.2cm] (m) {
    10&5\\
    10&25\\
    5&20\\
    25&20\\
};
\draw (m.north east) rectangle (m.south west);
\draw (m.north) -- (m.south);
\draw (m.east) -- (m.west);

\coordinate (a) at ($(m.north west)!0.25!(m.north east)$);
\coordinate (b) at ($(m.north west)!0.75!(m.north east)$);
\node[above=5pt of a,anchor=base] {Low Price};
\node[above=5pt of b,anchor=base] {High Price};

\coordinate (c) at ($(m.north west)!0.25!(m.south west)$);
\coordinate (d) at ($(m.north west)!0.75!(m.south west)$);
\node[left=2pt of c,text width=1cm]  {Low Price};
\node[left=2pt of d,text width=1cm]  {High Price};

\node[above=18pt of m.north] (firm b) {Firm B};
\node[left=1.6cm of m.west,rotate=90,align=center,anchor=center] {Firm A};

\node[above=5pt of firm b]  {Payoff Matrix};
\end{tikzpicture}

\end{document}

Answer 1

I cite my earlier post on TeXwelt answering the question Spieltheorie Auszahlungsmatrix mit Pfeilen zur Darstellung von Equilibria.

A quick solution with just the drawing commands referring to matrix elements:

\draw [-latex, blue, very thick]
    (m-1-2.center) edge (m-1-1)
    ($(m-2-1.south)+(-0.55,0)$) edge ($(m-4-1.north)+(-0.55,0)$)
    (m-3-1.east) edge (m-3-2.center)
    ($(m-4-2.north)+(-0.55,0)$) to ($(m-2-2.south)+(-0.55,0)$);
\end{tikzpicture}

You can tweak the calculation values. I needed calculating because of the varying alignment per row. I would have preferred twice as much columns but consistent alignment for easier reference.

The lines above give, with the original code: