game theory subgame box

Question

I am trying to make the grey boxes larger, but cannot succeed (large enough to include the playoffs). Would really appreciate some help.

Here is my code:

[![\documentclass\[11pt\]{article}
\usepackage\[utf8\]{inputenc}
\usepackage{multirow}
\usepackage\[margin=1in\]{geometry} 
\usepackage{amsmath,amsthm,amssymb,amsfonts}
 \usepackage{tikz}   %for game theory stuff
 \usepackage\[skip=1ex\]{caption}
\usetikzlibrary{calc}
\usepackage{istgame} 
\def\vpay#1#2{\begin{matrix}#1\\#2\end{matrix}}

\begin{document}


   \begin{center}
    \begin{istgame}
    \xtShowEndPoints
    \xtdistance{25mm}{70mm}
    \istrooto(0){$\text{Firm} \ 1$}
      \istb{BIG}\[l\]
      \istb{small}\[r\]
      \endist
      \xtdistance{25mm}{35mm}
    \istrooto(1)(0-1){$\text{Firm} \ 2$}
      \istb{Low}\[l\]
      \istb{High}\[r\]
      \endist
      \istrooto(2)(0-2){$\text{Firm} \ 2$}
      \istb{low}\[l\]
      \istb{high}\[r\]
      \endist
    \xtdistance{20mm}{10mm}
      \istrooto(a)(1-1){$\text{Firm} \ 1$}
      \istb{L}\[l\]{\vpay{8}{8}}
      \istb{H}\[r\]{\vpay{7}{7}}
      \endist
      \istrooto(b)(1-2){$\text{Firm} \ 1$}
      \istb{L}\[l\]{\vpay{6}{10}}
      \istb{H}\[r\]{\vpay{6}{7}}
      \endist
    \istrooto(c)(2-1){$\text{Firm} \ 1$}
      \istb{l}\[l\]{\vpay{7}{8}}
      \istb{h}\[r\]{\vpay{10}{6}}
      \endist
      \istrooto(d)(2-2){$\text{Firm} \ 1$}
      \istb{l}\[l\]{\vpay{5}{11}}
      \istb{h}\[r\]{\vpay{8}{7}}
      \endist
      \setxtinfosetstyle{dashed}
    \xtInfoset(a)(b)
    \xtInfoset(c)(d)
    \xtSubgameBox(1){(a)(b)(a-1)(b-1)(a-1)(b-2)(a-2)}
    \xtSubgameBox(2){(c)(d)(c-1)}
    %\xtSubgameBox(2){(2-1)(2-2)}\[inner sep=16pt\]
    %\xtSubgameBox(2){(2-1)(2-2)}\[solid,rounded corners=0pt,inner sep=16pt\]
    \end{istgame}

    \end{center}
    \end{document}][1]][1]

score 2 · Accepted Answer · answered Apr 03 '19 at 03:06

I followed the manual of istgame to where it talks about these experimental boxes. There it is suggested to move and enlarge the boxes. This is what I did, i.e. I added [yshift=-2ex] and [inner ysep=6ex]. I am not claiming this is elegant, but at least I can blame the manual for this choice.

\documentclass[11pt]{article}
\usepackage[utf8]{inputenc}
\usepackage[margin=1in]{geometry} 
\usepackage{amsmath}
\usepackage{istgame} 
\def\vpay#1#2{\begin{matrix}#1\\#2\end{matrix}}

\begin{document}
\begin{center}
\begin{istgame}
    \xtShowEndPoints
    \xtdistance{25mm}{70mm}
    \istrooto(0){$\text{Firm} \ 1$}
      \istb{BIG}[l]
      \istb{small}[r]
      \endist
      \xtdistance{25mm}{35mm}
    \istrooto(1)(0-1){$\text{Firm} \ 2$}
      \istb{Low}[l]
      \istb{High}[r]
      \endist
      \istrooto(2)(0-2){$\text{Firm} \ 2$}
      \istb{low}[l]
      \istb{high}[r]
      \endist
    \xtdistance{20mm}{10mm}
      \istrooto(a)(1-1){$\text{Firm} \ 1$}
      \istb{L}[l]{\vpay{8}{8}}
      \istb{H}[r]{\vpay{7}{7}}
      \endist
      \istrooto(b)(1-2){$\text{Firm} \ 1$}
      \istb{L}[l]{\vpay{6}{10}}
      \istb{H}[r]{\vpay{6}{7}}
      \endist
    \istrooto(c)(2-1){$\text{Firm} \ 1$}
      \istb{l}[l]{\vpay{7}{8}}
      \istb{h}[r]{\vpay{10}{6}}
      \endist
      \istrooto(d)(2-2){$\text{Firm} \ 1$}
      \istb{l}[l]{\vpay{5}{11}}
      \istb{h}[r]{\vpay{8}{7}}
      \endist
      \setxtinfosetstyle{dashed}
    \xtInfoset(a)(b)
    \xtInfoset(c)(d)
    \xtSubgameBox([yshift=-2ex]1){(a)(b)(a-1)(b-1)(a-1)(b-2)(a-2)}[inner ysep=6ex]
    \xtSubgameBox([yshift=-2ex]2){(c)(d)(c-1)}[inner ysep=6ex]
    \end{istgame}
\end{center}
\end{document}

Thanks a lot! I am going to cite this (that I used help in writing my homework) and I was wondering if you mind giving me your name? — Elen Khachatryan, Apr 03 '19 at 21:00
@ElenKhachatryan No need to cite this, I am just an anonymous marmot who is bored with hibernation. ;-) — , Apr 03 '19 at 21:03
Ok then, I will cite you as an Anonymous Marmot! :D Big thanks again! — Elen Khachatryan, Apr 03 '19 at 21:05

I. Cho · Answer 2 · 2019-05-01T11:06:38.923

To represent a subgame of an extensive game with the istgame package, you need to specify the root of the subgame and outermost terminal nodes. Since it does not seem that there exists a general rule to control the size of a box representing a subgame, we need to adjust the size manually. To do this, you can adjust inner sep (or inner xsep or inner ysep) of a box and shift the subroot, as mentioned in the manual.

Please note that, in the following example, players are printed in text mode by default and that you don't need to write down all the terminal nodes.

\documentclass{standalone}
\usepackage{amsmath}
\def\vpay#1#2{\begin{matrix}#1\\#2\end{matrix}}
\usepackage{istgame}
\begin{document}
\begin{istgame}
\xtShowEndPoints
\xtdistance{25mm}{70mm}
\istrooto(0){Firm 1}
  \istb{BIG}[al]  \istb{small}[ar]  \endist
\xtdistance{25mm}{35mm}
\istrooto(1)(0-1){Firm 2}
  \istb{Low}[al]  \istb{High}[ar]   \endist
\istrooto(2)(0-2){Firm 2}
  \istb{low}[al]  \istb{high}[ar]   \endist
\xtdistance{20mm}{10mm}
\istrooto(a)(1-1){Firm 1}
  \istb{L}[l]{\vpay{8}{8}}   \istb{H}[r]{\vpay{7}{7}}   \endist
\istrooto(b)(1-2){Firm 1}
  \istb{L}[l]{\vpay{6}{10}}  \istb{H}[r]{\vpay{6}{7}}   \endist
\istrooto(c)(2-1){Firm 1}
  \istb{l}[l]{\vpay{7}{8}}   \istb{h}[r]{\vpay{10}{6}}  \endist
\istrooto(d)(2-2){Firm 1}
  \istb{l}[l]{\vpay{5}{11}}  \istb{h}[r]{\vpay{8}{7}}   \endist
% \setxtinfosetstyle{dashed}
\xtInfoset(a)(b)
\xtInfoset(c)(d)
\xtSubgameBox([yshift=-2ex]1){(a-1)(b-2)}[inner ysep=7ex]
\xtSubgameBox([yshift=-2ex]2){(c-1)(d-2)}[inner ysep=7ex]
\end{istgame}
\end{document}

You can do the same thing without using \xtSubgameBox.

For example, \xtSubgameBox([yshift=-2ex]2){(c-1)(d-2)}[inner ysep=7ex] is just an abbreviation of the following codes:

\coordinate (xtsubroot) at ($([yshift=-2ex]2)+(0,-.3)$);
\node [rectangle,draw,dashed,inner sep=20pt,rounded corners=15pt,black!50,inner ysep=7ex] 
      [fit=(xtsubroot)(c-1)(d-2)]{};

Whichever is used depends on your choice.

Just in case where you want to make your game tree grow eastwards, you need to adjust your subgame box accordingly. (I have not found any general pattern to control the size of the box no matter what the tree growing direction is.) See also another example.

\documentclass[border=1pt]{standalone}
\usepackage{amsmath}
\def\vpay#1#2{\begin{matrix}#1\\#2\end{matrix}}
\usepackage{istgame}
\begin{document}
\begin{istgame}
\setistgrowdirection'{east}
\xtShowEndPoints
\xtdistance{25mm}{70mm}
\istrooto(0){Firm 1}
  \istb{BIG}[al]  \istb{small}[bl]  \endist
\xtdistance{25mm}{35mm}
\istrooto(1)(0-1){Firm 2}
  \istb{Low}[al]  \istb{High}[bl]   \endist
\istrooto(2)(0-2){Firm 2}
  \istb{low}[al]  \istb{high}[bl]   \endist
\xtdistance{20mm}{10mm}
\istrooto(a)(1-1){Firm 1}
  \istb{L}[a]{\vpay{8}{8}}   \istb{H}[b]{\vpay{7}{7}}   \endist
\istrooto(b)(1-2){Firm 1}
  \istb{L}[a]{\vpay{6}{10}}  \istb{H}[b]{\vpay{6}{7}}   \endist
\istrooto(c)(2-1){Firm 1}
  \istb{l}[a]{\vpay{7}{8}}   \istb{h}[b]{\vpay{10}{6}}  \endist
\istrooto(d)(2-2){Firm 1}
  \istb{l}[a]{\vpay{5}{11}}  \istb{h}[b]{\vpay{8}{7}}   \endist
\xtInfoset(a)(b)
\xtInfoset(c)(d)
\xtSubgameBox([xshift=-2ex]1){(a-1)(b-2)}%[inner ysep=7ex]
\xtSubgameBox([xshift=-2ex]2){(c-1)(d-2)}%[inner ysep=7ex]
\end{istgame}
\end{document}

game theory subgame box

2 Answers2