Drawing a game tree on Tikz

Question

I need to draw the following game tree on tikz. It's a bayesian game. Sorry for the pic, I made it on Paint.

So basically there are 2 players G and T, N is the nature that gives a chance for each type of player. The action of G is continuous, that's why I put the curve line.

So, my main doubr is to put the continuous set of action for player G and to put the same set of information for players of the same type. As it can be seen in the following pic:

 \documentclass[tikz,border=10pt,multi]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usetikzlibrary{trees}
\usetikzlibrary{calc}
\tikzset{
% Two node styles for game trees: solid and hollow
solid node/.style={circle,draw,inner sep=1.5,fill=black},
hollow node/.style={circle,draw,inner sep=1.5}
}
\begin{document}
\begin{tikzpicture}[font=\footnotesize,edge from parent/.style={draw,thick}]
% Two node styles: solid and hollow
\tikzstyle{solid node}=[circle,draw,inner sep=1.2,fill=black];
\tikzstyle{hollow node}=[circle,draw,inner sep=1.2];
% Specify spacing for each level of the tree
\tikzstyle{level 1}=[level distance=15mm,sibling distance=50mm]
\tikzstyle{level 2}=[level distance=15mm,sibling distance=25mm]
\tikzstyle{level 3}=[level distance=15mm,sibling distance=15mm]
\tikzstyle{level 4}=[level distance=15mm,sibling distance=10mm]
% The Tree
\node(0)[hollow node]{}
child{node[solid node]{}
child{node[solid node]{}
child{node[below]{$1,0$} edge from parent node[left]{$\gamma$}
child{node[below]{$2,3$} edge from parent node[right]{$\tal$}
edge from parent node[above left]{$P$}
}
%I need to put for options in the node
child{node[solid node]{}
edge from parent node[above right]{$N$}
}
edge from parent node[above left]{$\theta$}
}
child{node[solid node]{}
child{node[solid node]{}
child{node[below]{$1,0$} edge from parent node(m)[left]{$\gamma$}
child{node[below]{$2,3$} edge from parent node(n)[right]{$\tal$}
edge from parent node[above left]{$c$}
}
child{node[solid node]{}
edge from parent node[above right]{$N$}
}
edge from parent node[above right]{$1-\theta$}
}
% information sets
\drawloosely dotted,very thicktoout=-15,in=195;
% movers
\node[above,yshift=2]at(0){};
\foreach \x in {1,2} \node[above,yshift=2]at(0-\x){};
\node at($.5(m)+.5(n)$){1};
\end{tikzpicture}
\end{document}

I tried using this code here:

\begin{tikzpicture}
\tikzstyle{hollow node}=[circle,draw,inner sep=1.5]
\tikzstyle{solid node}=[circle,draw,inner sep=1.5,fill=black]
\tikzset{
red node/.style={circle,draw=red,fill=red,inner sep=1.2},
blue node/.style={rectangle,draw=blue,inner sep=2.5}
}
% Specify spacing for each level of the tree
\tikzstyle{level 1}=[level distance=15mm,sibling distance=40mm]
\tikzstyle{level 2}=[level distance=15mm,sibling distance=30mm]
\tikzstyle{level 3}=[level distance=15mm,sibling distance=15mm]
\tikzstyle{level 4}=[level distance=15mm,sibling distance=12mm]

\node[hollow node,label=above:{Natureza}]{}
child{node(1)[solid node]{}
child{node[solid node]{} edge from parent node[left]{$P$}}
child{node[solid node]{} edge from parent node[right]{$N$}}
edge from parent node[left,xshift=-3]{$\theta$}
}
child{node(2)[solid node]{}
child{node[solid node]{} edge from parent node[left]{$P$}}
child{node[solid node]{} edge from parent node[right]{$N$}}
edge from parent node[right,xshift=3]{$1-\theta$}
};
\node at ($(1)!.5!(2)$) {$Governo$};
\end{tikzpicture}

If anyone could help me, I would be glad.

Answer 1

It is not altogether clear what exactly you want changed and what exactly you are stuck on, even with the addition of code.

Personally, I would use Forest because I like it and it is easy to make it do things concisely and more-or-less automagically, depending on your requirements. You can also use TikZ code in the tree, since it is based on TikZ. Tree specifications are a lot more concise, however.

Here's an example which implements a configuration where the content specified for each node is split:

<label>:<edge label>

and the option

my arc

enables the drawing of the little green arcs. Hopefully this should get you started.

Then we can write

  [N, label=above:Natureza
    [G:\theta, my arc
      [N:P, name=a
        [T:\gamma[:A][:R]]
        [T:\tau[:A][:R]]
        [T:\phi[:A][:R]]
        [T:1-\gamma-\tau-\phi[:A][:R]]
      ]
      [:N, name=b]
    ]
    [G:1-\theta, my arc, before typesetting nodes={prepend'={a}, append'={b}}
    ]
  ]

to specify the main tree, adding the 'Governo' label by hand afterwards.

  \node [font=\itshape] at (!r |- !r1) {Governo};

The result is as follows:

With a judicious definition for copy name template we can implement a style, copy connect to join a node to its counterpart on the other side.

Then we can write

  [N, label=above:Natureza
    [G:\theta, my arc
      [N:P, name=a, for children=copy connect
        [T:\gamma[:A][:R]]
        [T:\tau[:A][:R]]
        [T:\phi[:A][:R]]
        [T:1-\gamma-\tau-\phi[:A][:R]]
      ]
      [:N, name=b]
    ]
    [G:1-\theta, my arc, before typesetting nodes={prepend'={a}, append'={b}}
    ]
  ]
  \node [font=\itshape] at (!r |- !r1) {Governo};

to produce

This works because the nodes on the right are copies of the nodes on the left and we've labelled our copies systematically by appending -c to the name.

Complete code:

\documentclass[border=10pt]{standalone}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{forest}
\usetikzlibrary{calc}
\tikzset{
  % Two node styles for game trees: solid and hollow
  solid node/.style={circle,draw,inner sep=1.5,fill=black},
  hollow node/.style={circle,draw,inner sep=1.5}
}
\begin{document}
\begin{forest}
  for tree={
    l sep'+=25pt,
    s sep'+=5pt,
  },
  before typesetting nodes={
    where content={}{}{
      split option={content}{:}{my label,my edge label},
      delay={content=},
    },
    delay={for descendants={if n children=0{}{solid node}}},
  },
  hollow node,
  my label/.style={
    if={isodd(n)}{label={[green!75!black, font=\small]left:#1}}{label={[green!75!black, font=\small]right:#1}}
  },
  my edge label/.style={
    if={isodd(n)}{edge label={node [midway, red, left, font=\scriptsize] {$#1$}}}{edge label={node [midway, red, right, font=\scriptsize] {$#1$}}}
  },
  my arc/.style={
    tikz+={
      \draw [green!75!black] ($()!0.3!(!l)$) [bend left] to ($()!0.3!(!1) + (-5pt,2.5pt)$);
    },
  },
  copy name template={#1-c},
  copy connect/.style={
    tikz+/.process={
      Ow {name}
      {
        \draw [orange] () [bend left=15] to (##1-c);
      }%
    },
  }
  [N, label=above:Natureza
    [G:\theta, my arc
      [N:P, name=a, for children=copy connect
        [T:\gamma[:A][:R]]
        [T:\tau[:A][:R]]
        [T:\phi[:A][:R]]
        [T:1-\gamma-\tau-\phi[:A][:R]]
      ]
      [:N, name=b]
    ]
    [G:1-\theta, my arc, before typesetting nodes={prepend'={a}, append'={b}}
    ]
  ]
  \node [font=\itshape] at (!r |- !r1) {Governo};
\end{forest}
\end{document}

Answer 2

You can also use the istgame package:

Edit: istgame v2.0

With the istgame v2.0, \istrootcntm (instead of \istcntm) and \xtCInfoset (curved information set) can improve codes a little. (discouraged to use obsolete \istcntm)

\begin{document}   

\begin{istgame}[font=\scriptsize]
\xtALPush{-2pt}{-2pt}
% top part
\xtdistance{15mm}{50mm}
\istroot(0)[chance node]{N}
  \istb{\theta}[al]
  \istb{1-\theta}[ar]
  \endist
% middle part: left
\cntmdistance*{15mm}{15mm}
\istrootcntm[-120](P1)(0-1)
  \istb{P}[l]  \endist
\istroot(N1)(0-1)<135>{G}
  \istb*<grow=-60>{N}[r]
  \endist
% middle part: right
\istrootcntm[-120](P2)(0-2)
  \istb{P}[l]
  \endist
\istroot(N2)(0-2)  
  \istb*<grow=-60>{N}[r]
  \endist
% lower part: left
\xtdistance{15mm}{10mm}
\istroot(PN1)(P1-1)[chance node]<180>{N}
  \istb{\gamma}[l]
  \istb{\tau}[l]
  \istb{\phi}[l]
  \istb{1-\gamma-\tau-\phi}[r]
  \endist
% lower part: right
\xtdistance{15mm}{10mm}
\istroot(PN2)(P2-1)[chance node]<180>{N}
  \istb{\gamma}[l]
  \istb{\tau}[l]
  \istb{\phi}[l]
  \istb{1-\gamma-\tau-\phi}[r]
  \endist
% bottom part
\xtdistance{10mm}{5mm}
\foreach \a in {1,2}
  {\foreach \b in {1,2,3,4}
     {\istroot(T\a\b)(PN\a-\b)<180>{T}
      \istb{A}[l]  \istb{B}[r]  \endist
     }
  }
% information sets
\foreach \c in {1,2,3,4}
  {\xtCInfoset[solid,thin,orange](T1\c)(T2\c)<1.2>
  }
\end{istgame}

\end{document}

Original answer (istgame v1.0)

%% full codes
\documentclass{standalone}

\usepackage{istgame}

\begin{document}   

\begin{istgame}[font=\scriptsize]
\xtALPush{-2pt}{-2pt}
% top part
\xtdistance{15mm}{50mm}
\istroot(0)[chance node]{N}
  \istb{\theta}[al]
  \istb{1-\theta}[ar]
  \endist
% middle part: left
\istcntm[-120](cntm)(0-1)[green]+15mm..15mm+
\istroot[-120](P1)(cntm)<135>{G}+15mm..15mm+
  \istb{P}[l]
  \endist
\istroot(N1)(cntm)  
  \istb*<grow=-60>{N}[r]
  \endist
% middle part: right
\istcntm[-120](cntm)(0-2)[green]+15mm..15mm+
\istroot[-120](P2)(cntm)<45>{G}+15mm..15mm+
  \istb{P}[l]
  \endist
\istroot(N2)(cntm)  
  \istb*<grow=-60>{N}[r]
  \endist
% lower part: left
\xtdistance{15mm}{10mm}
\istroot(PN1)(P1-1)[chance node]<180>{N}
  \istb{\gamma}[l]
  \istb{\tau}[l]
  \istb{\phi}[l]
  \istb{1-\gamma-\tau-\phi}[r]
  \endist
\xtdistance{10mm}{5mm}
\istroot(T11)(PN1-1)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
\istroot(T12)(PN1-2)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
\istroot(T13)(PN1-3)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
\istroot(T14)(PN1-4)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
% lower part: right
\xtdistance{15mm}{10mm}
\istroot(PN2)(P2-1)[chance node]<180>{N}
  \istb{\gamma}[l]
  \istb{\tau}[l]
  \istb{\phi}[l]
  \istb{1-\gamma-\tau-\phi}[r]
  \endist
\xtdistance{10mm}{5mm}
\istroot(T21)(PN2-1)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
\istroot(T22)(PN2-2)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
\istroot(T23)(PN2-3)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
\istroot(T24)(PN2-4)<180>{T}
  \istb{A}[l]  \istb{R}[r]  \endist
% information sets
\xtInfoset[solid,thin,orange,bend left=20](T11)(T21)
\xtInfoset[solid,thin,orange,bend left=20](T12)(T22)
\xtInfoset[solid,thin,orange,bend left=20](T13)(T23)
\xtInfoset[solid,thin,orange,bend left=20](T14)(T24)
\end{istgame}

\end{document}

The istgame environment is just like the tikzpicture environment. For the bottom part of this tree, you can use \foreach to repeat things. A complete example is as follows:

%% shortened codes using \foreach
\documentclass{standalone}

\usepackage{istgame}

\begin{document}   

\begin{istgame}[font=\scriptsize]
\xtALPush{-2pt}{-2pt}
% top part
\xtdistance{15mm}{50mm}
\istroot(0)[chance node]{N}
  \istb{\theta}[al]
  \istb{1-\theta}[ar]
  \endist
% middle part: left
\istcntm[-120](cntm)(0-1)[green]+15mm..15mm+
\istroot[-120](P1)(cntm)<135>{G}+15mm..15mm+
  \istb{P}[l]
  \endist
\istroot(N1)(cntm)  
  \istb*<grow=-60>{N}[r]
  \endist
% middle part: right
\istcntm[-120](cntm)(0-2)[green]+15mm..15mm+
\istroot[-120](P2)(cntm)<45>{G}+15mm..15mm+
  \istb{P}[l]
  \endist
\istroot(N2)(cntm)  
  \istb*<grow=-60>{N}[r]
  \endist
% lower part: left
\xtdistance{15mm}{10mm}
\istroot(PN1)(P1-1)[chance node]<180>{N}
  \istb{\gamma}[l]
  \istb{\tau}[l]
  \istb{\phi}[l]
  \istb{1-\gamma-\tau-\phi}[r]
  \endist
% lower part: right
\xtdistance{15mm}{10mm}
\istroot(PN2)(P2-1)[chance node]<180>{N}
  \istb{\gamma}[l]
  \istb{\tau}[l]
  \istb{\phi}[l]
  \istb{1-\gamma-\tau-\phi}[r]
  \endist
% bottom part
\xtdistance{10mm}{5mm}
\foreach \a in {1,2}
  {\foreach \b in {1,2,3,4}
     {\istroot(T\a\b)(PN\a-\b)<180>{T}
      \istb{A}[l]  \istb{B}[r]  \endist
     }
  }
% information sets
\foreach \c in {1,2,3,4}
  {\xtInfoset[solid,thin,orange,bend left=20](T1\c)(T2\c)
  }
\end{istgame}

\end{document}