multirow and multicolumn table

Question

Is it possible to put the circled (-1, 1) on the same last row as the other values? Thank you for your help!!

\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} & \underset{s_1 \in S_1}{min} \, u(s_1, s_2) \\\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@{}}{$\underset{s_2 \in S_2}{min} \, u(s_1, s_2)$} & & 1 &1 & \multicolumn{1}{l}{\tikz\node[draw,rounded corners=5pt,minimum width=1cm]{-1,1};}
\end{tabular}
\end{table}

\end{document}

Answer 1

This could be a solution:

\documentclass[a4paper]{article}
\usepackage{geometry} \geometry{a4paper, top=25mm, left=25mm, right=25mm, bottom=20mm, headsep=10mm, footskip=12mm} 
\usepackage{amsmath}
\usepackage{multirow,array}
\usepackage{tikz}

\newcommand\mybox[3][]{%
    \tikz[anchor=base,baseline]\node[inner sep=2pt,draw=#2,#1]{$\displaystyle#3\mathstrut$};}
\colorlet{mycol}{black}

\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} & \underset{s_1 \in S_1}{min} \, u(s_1, s_2) \\\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@{}}{$\underset{s_2 \in S_2}{min} \, u(s_1, s_2)$} & & 1 &1 & 
            \multicolumn{1}{l}{\mybox[rounded corners]{mycol}{-1,1}}

        \end{tabular}
    \end{table}

\end{document}

Answer 2

Here is a solution with {NiceTabular} of nicematrix.

\documentclass{article}
\usepackage{nicematrix}

\begin{document}

\renewcommand{\arraystretch}{1.3}
\begin{NiceTabular}{ccccl}
                      &   & \Block{1-2}{Player II} \\
                      &   & H    & T    & \rlap{$\min\limits_{s_1 \in S_1}u(s_1,s_2)$} \\
\Block{2-1}{Player I} & H & \Block[hvlines]{2-2}{}
                            $1$  & $-1$ & $-1$ \\
                      & T & $-1$ & $-1$ & $-1$ \\
\smash{$\min\limits_{s_2 \in S_2} u(s_1,s_2)$ }
                      &   & $1$  & $1$ & \Block[draw,rounded-corners]{}{$-1,1$} \\
\end{NiceTabular}

\end{document}