How to add nodes on the axis in axis environment in TikZ?

The following are my code. I used the axis environment for better axis style. I try to add nodes at g^W=g^L, which is a point on the y-axis, but the axis environment seemes to cut off anything outside the axis. What should I do?

\documentclass[11pt]{article}
\usepackage{pgfplots}
\begin{document}

\begin{figure}
\centering
\begin{tikzpicture}[scale = 1.2]
\begin{axis}[xmin=0,xmax=10,ymin=0,ymax=7,
axis lines = left, axis line style = thick,  unit vector ratio=1 1 1, xtick={0,8},
xticklabels = {$p^w=0$, $p^w=1$},
ytick={1.5,3,5.5},
yticklabels = {$g^L-\beta$,$g^W=g^L$,$g^w+\alpha$}]
\addplot[mark=none, dashed] coordinates {(8, 0) (8, 7)};

\node[black,right] at (axis cs:8,1.5){\small{$W=0$}};
\node at (axis cs:8,1.5) [circle, scale=0.3, draw=black!80,fill=black!80] {};
\node at (axis cs:8,3) [circle, scale=0.3, draw=black!80,fill=black!80] {};
\node at (0,3.5) [circle, scale=0.3, draw=black!80,fill=black!80] {};
\end{axis}
\end{tikzpicture}
\caption{A caption.}
\end{figure}


\end{document}

clip mode=individual

to the axis options, the diagrams (with addplot) will be clipped, but the nodes will not.
Otherwise, clip = false will avoid any clipping.
PS: you need a \pgfplotsset{compat=1.9} or whatever added, to avoid surprises...
• clip means to cut off all that will go outside the axis range. Imagine a function like 1/x which will go unbounded otherwise... – Rmano Apr 2 '16 at 14:23