How to visually present a simultaneous game with continuous strategies
This thread has some game trees. In case you want put them on your documents, you can do like this (using LaTeX with istgame package):



\documentclass{standalone}

\usepackage{istgame}

\begin{document}

\begin{istgame}[font=\scriptsize]
\setistgrowdirection{east}
\cntmdistance{20mm}{20mm}
\cntmAistb{q_1=0}[at end,below]{q_1=1,000}[at end,above]
\istrootcntmA(0){1}
  \istbA[draw=none]
  \endist
\cntmAistb{q_2=0}[at end,below]{q_2=1,000}[at end,above]
\istrootcntmA(1)(0-1)&lt;[xshift=3pt]90&gt;{2}
  \istbA[draw=none]{}{\pi_1,\pi_2}
  \endist
\end{istgame}

\end{document}




\documentclass{standalone}

\usepackage{amsmath}
\usepackage{istgame}

\begin{document}

\NewDocumentCommand\vpay{m}
{ \begin{matrix} #1 \end{matrix} }

\begin{istgame}[scale=1.5,font=\scriptsize]
\cntmApreset{.9}
\cntmdistance{15mm}{20mm}
\istrootcntmA(0)[null node]{1}
  \istbA(.977)[-&gt;,thick]{q_1}[r]
  \istbm
  \endist
\cntmAInfosetO[thick,dashed](0)[-11](2em)
\istrootcntmA(1)(0-1)[null node]&lt;180&gt;{2}
  \istbm
  \istbA(.977)[-&gt;,thick]{q_2}[r]
    {\vpay{\pi_1(q_1,q_2)\\\pi_2(q_1,q_2)}}
  \endist
\end{istgame}

\end{document}




\documentclass{standalone}

\usepackage{amsmath}
\usepackage{istgame}

\begin{document}

\NewDocumentCommand\vpay{m}
{ \begin{matrix} #1 \end{matrix} }

\begin{istgame}
\xtdistance{15mm}{40mm}
\cntmdistance{15mm}{30mm}
\cntmApreset[draw=none]{1}[red!50,opacity=.2]
\istroot(0){Challenger}
  \istb{In}[al]  \istb{Out}[ar]  \endist
\cntmAistb[draw=none]
\istrootcntmA(1)(0-1)&lt;135&gt;{Incumbent}
  \istbA{q_I}[left]  \endist
\cntmAInfosetO(1)
\cntmAistb[draw=none]
\istrootcntmA(2)(0-2)&lt;45&gt;{Incumbent}
  \istbA*{q_I}[left]
    {\vpay{\pi_C(0,q_I)\\\pi_I(0,q_I)}}
  \endist
\cntmApreset[draw=none]{1}[blue!50,opacity=.2]
\cntmAistb[draw=none]
\istrootcntmA(3)(1-1)&lt;180&gt;{Challenger}
  \istbA*{q_C}[midway,left]
    {\vpay{\pi_C(q_C,q_I)\\ \pi_I(q_C,q_I)}}
  \endist
\end{istgame}

\end{document}