Drawing a table using multirow and multicolumn

Question

I would really like to draw a table like on the photo. Everything I have tried does not work. Maybe I do something wrong right at the beginning. I only got the table you can see in the code below. There is still a lot to do for getting a table like on the photo. But I just do not understand how to get there. It is all new for me and I hope you are not angry about the question. (and sorry for my bad English). Thank you for your help!

\documentclass[a4paper, fontsize=11pt]{scrbook}
\usepackage{geometry} \geometry{a4paper, top=25mm, left=25mm, right=25mm, bottom=20mm, headsep=10mm, footskip=12mm} 
\usepackage[ngerman]{babel}  
\usepackage[T1]{fontenc}         
\usepackage[latin1]{inputenc}   
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multirow,array}
\usepackage{arydshln}          
\dashlinegap=1pt                   
\usepackage{acronym}

\begin{document}

\begin{table}
\renewcommand\arraystretch{1.5}
\begin{tabular}{*{5}{>{$}c<{$}|}}
\multicolumn{2}{c}{} & \multicolumn{3}{c}{Spieler 2} \\ \cline{3-5}
\multicolumn{1}{c}{} &  & s_{21}  & s_{22} & s_{23} \\ \cline{2-5}
\multirow{3}*{Spieler 1}
& s_{11} & 1 & 6 & 0 \\ \cline{2-5}
& s_{12} & 2 & 0 & 3 \\ \cline{2-5}
& s_{12} & 3 & 2 & 4 \\ \cline{2-5}
\end{tabular}
\end{table}

\end{document}

Answer 1

The ovale frame can be drawn with tikz

Code

\documentclass[a4paper]{article}
\usepackage{geometry} \geometry{a4paper, top=25mm, left=25mm, right=25mm, bottom=20mm, headsep=10mm, footskip=12mm} 
\usepackage[ngerman]{babel}  
\usepackage[T1]{fontenc}         
\usepackage[latin1]{inputenc}   
\usepackage{amsmath}
\usepackage{amssymb}
\usepackage{multirow,array}
\usepackage{arydshln}  
\usepackage{tikz}        
\dashlinegap=1pt                   
\usepackage{acronym}

\begin{document}

\begin{table}
\renewcommand\arraystretch{1.5}
\setlength{\tabcolsep}{4mm}
\begin{tabular}{*{5}{>{$}c<{$}}}
 & & \multicolumn{2}{c}{Player II}& \\ 
 & & \multicolumn{1}{c}{H}  & \multicolumn{1}{c}{T} & min_{s_{II}}S_{II}u_I(S_I,S_{II})\\\cline{3-4}
\multirow{2}*{Player I}
& H & \multicolumn{1}{|c|}{1} & \multicolumn{1}{c|}{-1} &\multicolumn{1}{l}{-1} \\ \cline{3-4}
& T & \multicolumn{1}{|c|}{-1} & \multicolumn{1}{c|}{-1} &\multicolumn{1}{l}{-1} \\ \cline{3-4}
\multicolumn{1}{r@{}}{$min_{s_{I}}S_{II}u_I(S_I,S_{II})$} & & 1 &1 & \multicolumn{1}{l}{\tikz\node[draw,rounded corners=5pt,minimum width=1cm]{-1,1};}
\end{tabular}
\end{table}

\end{document}