☰

后续：使用 Tikz 和 Forest 绘制具有曲线信息集和多个节点的游戏树

tag-icon • tag-icon tikz-pgf tikz-trees forest draw game-tree
后续：使用 Tikz 和 Forest 绘制具有曲线信息集和多个节点的游戏树

这是来自绘制游戏树-Tikz 还是 Forest？

我想要绘制的顺序游戏树是这样的： 在此处输入图片描述

我正在使用 tikz 和 forest 来绘制它，但距离它还很远。具体来说：我想 1. 在不同的节点中包含不同玩家的名称（简单地说是“玩家 1”和“玩家 2”）；2. 为玩家 1 创建第二个节点（包含信息集）（其中策略是“提出建议”）；3. 正确绘制最后两个信息集（用蓝色和红色突出显示）。

我正在发送迄今为止的代码：

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage[edges]{forest}
\usepackage[outline]{contour}
\usetikzlibrary{fit,shapes.misc,arrows.meta,positioning}
\tikzset{rconnect/.style args={#1 and #2}{insert path={
($(#1)+    (270+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/r    adius})$) 
arc(270+\pgfkeysvalueof{/tikz/rconnect/angle}:90+\pgfkeysvalueof{/tikz/rcon    nect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[out=\pgfkeysvalueof{/tikz/rconnect/angle},in=180-    \pgfkeysvalueof{/tikz/rconnect/angle}] 
($(#2)+(90-    \pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius    })$) 
arc(90-\pgfkeysvalueof{/tikz/rconnect/angle}:-90-    \pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius    })
to[in=\pgfkeysvalueof{/tikz/rconnect/angle},out=180-    \pgfkeysvalueof{/tikz/rconnect/angle}] 
cycle}},rconnect/.cd,radius/.initial=6.5pt,angle/.initial=-12}

\begin{document}

\begin{forest}
for tree={s sep=0.1cm,l sep=1.2cm,font=\scriptsize,
where n children=0{align=center,draw,edge={thick,-{Circle}}}                {circle,fill,inner sep=0pt,minimum size=2mm},
where n=1{edge label={node[midway,above left=0pt,font=\scriptsize]{S}}}        {edge
label={node[midway,above right=0pt,font=\scriptsize]{E}}},
edge={thick}
}
  [,label=above:Nature,alias=T
   [,alias=L
   [,alias=LL
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,alias=LR
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
   [,alias=R
    [,alias=RL
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,alias=RR
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
  ]
\node[draw,dashed,rounded rectangle,fit=(L) (R)] (F1){};  
\node[draw,dashed,rounded rectangle,fit=(LR) (RL)]{};  
\draw[dashed] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1] [rconnect=LL and RR];
\end{forest}

\end{document}

答案1

另一种解决方案是使用游戏包裹：

在此处输入图片描述

\documentclass{standalone}

\usepackage{amsmath}
\usepackage{makecell}

\usepackage{istgame}

\NewDocumentCommand\mact{m}
{\makecell[c]{#1}}
\NewDocumentCommand\mpay{m}
{\begin{pmatrix}#1\end{pmatrix}}

\begin{document}

\begin{istgame}[font=\footnotesize]
\setistmathTF*001
\xtShowEndPoints
% top part
\xtdistance{25mm}{120mm}
\istroot(0)[chance node]{Nature}
  \istb{\mact{$R=O$\\(Cooperative\\Player)}}[above left,xshift=-10pt]
  \istb{\mact{$R=\bar R$\\(Competitive\\Player)}}[above right,xshift=10pt]  \endist
\xtdistance{25mm}{50mm}
\istroot(A)(0-1)%<180>{Player 1}
  \istb{\mact{Introduce\\Proposal}}[l]  \endist
\istroot(B)(0-2)%<0>{Player 1}
  \istb{\mact{Introduce\\Proposal}}[r]  \endist
% left part
\xtdistance{25mm}{60mm}
\istroot(A0)(A-1)<180>{Player 2}
  \istb{Go}[al]  \istb{Stay}[ar]  \endist
\xtdistance{25mm}{30mm}
\istroot(A1)(A0-1)<0>{$(B-C,O)$}
  \istb{\mact{Introduce\\Proposal\\(I)}}[al]  \istb{\mact{Delay\\(D)}}[ar]  \endist
\istroot(A2)(A0-2)<180>{$(B,X)$}
  \istb{I}[al]  \istb{D}[ar]  \endist
\xtdistance{25mm}{15mm}
\istroot(A3)(A1-1)<180>{Player 2}
  \istb{Go (G)}[l]{\mpay{B-C\\O}}  \istb{Stay (S)}[r]{\mpay{B\\X}}  \endist
\istroot(A4)(A1-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B-L\\X-L}}     \istb{S}[r]{\mpay{B-C\\O}}       \endist
\istroot(A5)(A2-1)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\X}}         \istb{S}[r]{\mpay{B-L\\X-L}}     \endist
\istroot(A6)(A2-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\O}}         \istb{S}[r]{\mpay{L\\O}}         \endist
% right part
\xtdistance{25mm}{60mm}
\istroot(B0)(B-1)<180>{Player 2}
  \istb{Go}[al]  \istb{Stay}[ar]  \endist
\xtdistance{25mm}{30mm}
\istroot(B1)(B0-1)<0>{$(B-C,\bar R)$}
  \istb{I}[al]  \istb{D}[ar]  \endist
\istroot(B2)(B0-2)<180>{$(B,X)$}
  \istb{I}[al]  \istb{D}[ar]  \endist
\xtdistance{25mm}{15mm}
\istroot(B3)(B1-1)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\-L}}        \istb{S}[r]{\mpay{B-L\\R-L}}  \endist
\istroot(B4)(B1-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\\bar R}}    \istb{S}[r]{\mpay{B\\O}}      \endist
\istroot(B5)(B2-1)<180>{Player 2}
  \istb{G}[l]{\mpay{B\\\bar R}}    \istb{S}[r]{\mpay{B-L\\L}}    \endist
\istroot(B6)(B2-2)<180>{Player 2}
  \istb{G}[l]{\mpay{B-R\\\bar R}}  \istb{S}[r]{\mpay{B-L\\X-L}}  \endist
% information sets
\setxtinfosetstyle{dashed}
\xtInfosetO(A)(B){Player 1}(1.5em)
\xtCInfosetO[blue](A1)!.35!(B1)<1.15>{Player 1}(1.5em)
\xtCInfosetO[red](A2)!.5!(B2)<.75>{Player 1}(1.5em)
\end{istgame}

\end{document}

答案2

发布此内容的主要动机是消除样式中添加的空格rconnect，这些空格会导致上述代码出现错误。除此之外，您还可以使用标签添加玩家。我不明白另一个要求，因为我不是在研究博弈论，所以我不知道这些术语是什么意思。

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage[edges]{forest}
\usepackage[outline]{contour}
\usetikzlibrary{fit,shapes.misc,arrows.meta,positioning}
\tikzset{rconnect/.style args={#1 and #2}{insert path={
($(#1)+(270+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(270+\pgfkeysvalueof{/tikz/rconnect/angle}:90+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[out=\pgfkeysvalueof{/tikz/rconnect/angle},in=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
($(#2)+(90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(90-\pgfkeysvalueof{/tikz/rconnect/angle}:-90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[in=\pgfkeysvalueof{/tikz/rconnect/angle},out=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
cycle}},rconnect/.cd,radius/.initial=6.5pt,angle/.initial=-12}

\begin{document}

\begin{forest}
for tree={s sep=0.1cm,l sep=1.2cm,font=\scriptsize,
where n children=0{align=center,draw,edge={thick,-{Circle}}}                {circle,fill,inner sep=0pt,minimum size=2mm},
where n=1{edge label={node[midway,above left=0pt,font=\scriptsize]{S}}}        {edge
label={node[midway,above right=0pt,font=\scriptsize]{E}}},
edge={thick}
}
  [,label=above:Nature,alias=T
   [,label=above left:Player 1,alias=L
   [,label=above left:Player 2,alias=LL
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=LR
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
   [,label=above right:Player 1,alias=R
    [,label=above left:Player 2,alias=RL
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=RR
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
  ]
\node[draw,dashed,rounded rectangle,fit=(L) (R)] (F1){};  
\draw[dashed,blue] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LL and RL];
\draw[dashed,red] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LR and RR];
\end{forest}
\end{document}

在此处输入图片描述

至于你的评论：uisng这个很好的答案可以这样做：将左侧或右侧的项目存储在列表中，然后根据级别附加项目。（如果你真的需要的话，您可以用其他东西替换“Hibernate”。;-)

\documentclass[tikz,border=3.14mm]{standalone}
\usepackage[edges]{forest}
\usepackage[outline]{contour}
\usetikzlibrary{fit,shapes.misc,arrows.meta,positioning}
\tikzset{rconnect/.style args={#1 and #2}{insert path={
($(#1)+(270+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(270+\pgfkeysvalueof{/tikz/rconnect/angle}:90+\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[out=\pgfkeysvalueof{/tikz/rconnect/angle},in=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
($(#2)+(90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})$)
arc(90-\pgfkeysvalueof{/tikz/rconnect/angle}:-90-\pgfkeysvalueof{/tikz/rconnect/angle}:\pgfkeysvalueof{/tikz/rconnect/radius})
to[in=\pgfkeysvalueof{/tikz/rconnect/angle},out=180-\pgfkeysvalueof{/tikz/rconnect/angle}]
cycle}},rconnect/.cd,radius/.initial=6.5pt,angle/.initial=-12}

\begin{document}
\edef\LstLeft{0,"$p$","Go","Wait","A"}
\edef\LstRight{0,"$1-p$","Stay","Hibernate","B"}
\begin{forest}
for tree={s sep=0.1cm,l sep=1.2cm,font=\scriptsize,
where n children=0{align=center,draw,edge={thick,-{Circle}}}{circle,fill,inner sep=0pt,minimum size=2mm},
before drawing tree={
        if level=0{}{
          if n'=1{
            edge label/.wrap pgfmath arg={node [midway, right=.5em]
            {\pgfmathparse{{\LstLeft}[#1]}\pgfmathresult}}{level()},
          }{
            edge label/.wrap pgfmath arg={node [midway, left=.5em] 
            {\pgfmathparse{{\LstRight}[#1]}\pgfmathresult}}{level()},
          },
        }{}
      },
%where n=1{edge label={node[midway,above left=0pt,font=\scriptsize]{S}}}{edge label={node[midway,above right=0pt,font=\scriptsize]{E}}},
edge={thick}
}
  [,label=above:Nature,alias=T
   [,label=above left:Player 1,alias=L
   [,label=above left:Player 2,alias=LL
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=LR
     [
      [{$B-C$ \\ $0$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
   [,label=above right:Player 1,alias=R
    [,label=above left:Player 2,alias=RL
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
    [,label=above right:Player 2,alias=RR
     [
      [{$B-C$ \\ $\bar{R}$}]
      [{$B$ \\ $X$}]
     ]
     [
      [{$B-L$ \\ $R-L$}]
      [{$B-L$ \\ $X-L$}]
     ]
    ]
   ]
  ]
\node[draw,dashed,rounded rectangle,fit=(L) (R)] (F1){};  
\draw[dashed,blue] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LL and RL];
\draw[dashed,red] let \p1=($(F1.north)-(F1.center)$) in
 [/tikz/rconnect/radius=\y1]  [rconnect=LR and RR];
\end{forest}
\end{document}

在此处输入图片描述

相关内容