Vertical alignment of a tabular in an equation

Question

I am using the package sgame to format normal form games. The games are commonly formatted inside a figure but I would like to use them in an equation. I am having a problem with the vertical spacing of punctuation.

Here is the code I use:

\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
\end{game}
.
\end{equation}

\end{document}

Here is the result:

I like the alignment of the equation number but not of the period. I would like to have the period aligned with the text in the last row of the table. The distance is 0.3\baselineskip from the bottom horizontal line but it is not a fixed distance from the baseline.

This is what I am after:

Answer 1

\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}

Answer 2

It turns out that the baseline was not 0.3\baselineskip from the bottom of the game. The sgame package reimplements the array structure with two major differences:

1. the text is centered in the cell instead of having the baseline at 30%

2. the rules around the array can collide with the text, they seem to be in a sort of overlay

The following solution deals with these two differences and work when changing the values of \gamestretch and arrayrulewidth.

\documentclass{article}

\usepackage{calc}
\usepackage{color}
\usepackage{sgamevar}

\newcommand{\punctuategame}[2]{%
  \setbox0 = \hbox{#1}% box containing the whole game
  \setbox1=\hbox{I}% box used to determined the height of text in a cell
  \newlength{\vdisp}% vertical displacement of punctuation
  \setlength{\vdisp}{-\dp0 - \arrayrulewidth + \gamestretch \baselineskip / 2 - \ht1 / 2}%
  \newlength{\hdisp}% horizontal displacement of punctuation
  \setlength{\hdisp}{0.5\arrayrulewidth}%
  \mbox{#1}% placing the game
  \raisebox{\vdisp}{\hspace{\hdisp}\mbox{#2}}}% placing punctuation

\begin{document}

\begin{equation}
\punctuategame{
\begin{game}{3}{2}
  \> F     \> O    \\
F \> 2, 2  \> 0, 1 \\
O \> 0, 0  \> 1, 3 \\
P \> 0, 0  \> 1, 3
\end{game}
}{.}
\end{equation}

\end{document}