Vertical alignment of a tabular in an equation

\documentclass{article}

\usepackage{color}
\usepackage{sgame}
\gamemathtrue

\begin{document}

\begin{equation}
\begin{game}{3}{2}
  & F     & O    \\
F & 2, 2  & 0, 1 \\
O & 0, 0  & 1, 3 \\
P & 0, 0  & 1, 3\rlap{\quad.}
\end{game}
\end{equation}

\end{document}