Complex probability tree

Question

For a Game theory exercise I have been trying to recreate the following tree using the TiKz package. I don't know if this package is the right approach but here is the tree I am attempting to replicate:

If someone could provide an example of the code needed to do this specific kind of tree it would be of great help, as I can copy it to multiple other examples I have to work.

I am particularly struggling with the labels in the branches, the dotted line and the horizontal line at the beginning. This is why I do not share any attempt of code as it is all looking off and it would be detrimental to the post.

In case my preamble is needed please find it below:

**EDIT: PREAMBLE CLEANED

\documentclass[12pt, a4 paper]{article}

\usepackage{multicol} %Needed for \PDgame
\usepackage{multirow}
\usepackage{wrapfig}
\usepackage[english]{babel}
\usepackage[utf8]{inputenc}
\usepackage{amsmath,amssymb}
\usepackage{parskip}
\usepackage{graphicx}
\usepackage{mathtools}
\usepackage{graphicx}
\usepackage{verbatim}
\usepackage{subcaption}
\usepackage{indentfirst}
\usepackage{tikz}

% Margins
\usepackage[inner=2.0cm,outer=2.0cm,top=2.5cm,bottom=2.5cm]{geometry}
% Colour table cells
\usepackage[table]{xcolor}


\setlength{\marginparwidth}{2cm}
\begin{document}
\end{document}

Answer 1

Answer adapted from this question. To connect nodes simply name them and then you can draw lines between them. This is how the dashed line is done. The top two lines are just hard coded. There's probably a way to do it more automatically but I don't know it.

\documentclass[border=25]{standalone}
\usepackage{tikz}
\usetikzlibrary{calc}
\begin{document}

\tikzset{
    solid node/.style={circle,draw,inner sep=1.2,fill=black},
}

\begin{tikzpicture}[font=\footnotesize]
    \tikzset{
        level 1/.style={level distance=15mm,sibling distance=65mm},
        level 2/.style={level distance=15mm,sibling distance=30mm},
        level 3/.style={level distance=15mm,sibling distance=15mm},
        level 4/.style={level distance=15mm,sibling distance=10mm},
  }

    \node(top)[solid node,label=above left:{1},red]{}
        child{[red]node[solid node,label=above:{1}]{}
        child{[black]node[solid node,label=left:{2}]{}
        child{[red]node[solid node,label=below:{\((6, 0)\)}]{}edge from parent node[left]{\(\alpha_2\)}}
        child{[red]node[solid node,label=below:{\((3, 1)\)}]{}edge from parent node[right]{\(\beta_2\)}}
        edge from parent node[left]{\(A_1\)}
    }
        child{node[solid node,label=below:{\((4,1)\)}]{}  % This is the branch that ends early
        edge from parent node[right]{\(B_1\)}
    }
        edge from parent node[left,xshift=-10]{\(a_1\)}
    }
        child{node[solid node,label=above:{2}]{}
        child{[red]node(A2)[solid node]{}
        child{node[solid node,black,label=below:{\((3, 3)\)}]{}edge from parent node[left]{\(\alpha_1\)}}
        child{[black]node[solid node,label=below:{\((1,5)\)}]{}edge from parent node[right]{\(\beta_1\)}}
        edge from parent node[left]{\(A_2\)}
    }
        child{node(B2)[solid node]{}
        child{[red]node[solid node,label=below:{\((4, 2)\)}]{}edge from parent node[left]{\(\alpha_1\)}}
        child{node[solid node,label=below:{\((5,1)\)}]{}edge from parent node[right]{\(\beta_1\)}}
        edge from parent node[right]{\(B_2\)}
    }
        edge from parent node[right,xshift=10]{\(b_1\)}
    };
    \draw[dashed] (A2) -- (B2) node[midway, above] {1};
    \coordinate (right angle) at ($(top) + (0, 1.5)$);
    \draw[red] (top) -- (right angle) node[midway, right,black] {\(C\)};
    \node[solid node,red,label=above:{2}] at (right angle) {};
    \draw[red] (right angle) -- ($(right angle) + (1.5, 0)$) node[black, midway, above] {\(S\)} node[below,black] {\((1, 2)\)};
    
\end{tikzpicture}
\end{document}

Answer 2

You might also use forest.

\documentclass{article}
\usepackage[edges]{forest}
\newcommand{\ur}[2][red]{\textcolor{#1}{\underline{\textcolor{black}{#2}}}}
\begin{document}
\begin{forest}
er/.style={edge=red},r/.style={color=red},rer/.style={r,er},
el/.style={edge label={node[midway,auto,color=black]{\ensuremath{#1}}}},
el'/.style={edge label={node[midway,auto,color=black,swap]{\ensuremath{#1}}}},
for tree={l sep+=2em,s sep+=2em,
    if n children=0{math content}{circle,inner sep=1pt,fill},
    if level=3{tier=bottom}{}}
[,r,label={90:1},alias=r,
    tikz+={\path[draw=red] ()-- node[auto]{$S$} ++ (2,0) node[below]{$(1,\ur{2})$};}
 [,rer,el={C},label={135:1}
  [,er,el'={\alpha},label={90:1}
   [,el'={A_1},label={135:2}
    [{(6,0)},el'={\alpha_2}]
    [{(3,1)},el={\beta_2}]
   ]
   [{(4,\ur{1})},er,el={B_1}
   ]
  ]
  [,label={90:2},el={b_1}
   [,er,el'={A_2},tikz+={\path[draw,dotted] () -- (!s);}
    [{(3,3)},er,el'={\alpha_1}]
    [{(1,5)},el={\beta_1}]
   ]
   [,el={B_2}
    [{(4,2)},er,el'={\alpha_1}]
    [{(1,5)},el={\beta_1}]
   ]
  ]
 ] 
]
\end{forest}
\end{document}

Answer 3

Using the istgame package, you can do this:

1. Draw the game tree:

\documentclass[tikz]{standalone}
    
\usepackage{istgame}

\begin{document}

\begin{istgame}
\xtdistance{10mm}{20mm}
\istroot[-45](0){2}
  \istb{C}[r]                \istb{S}[a]{(1,2)}[b]     \endist
\xtdistance{15mm}{60mm}
\istroot(1)(0-1)<135>{1}
  \istb{a_1}[al]             \istb{b_1}[ar]            \endist
\xtdistance{15mm}{30mm}
\istroot(2)(1-1){1}
  \istb{A_1}[al]             \istb{B_1}[ar]{(4,1)}     \endist
\istroot(3)(1-2){2}
  \istb{A_2}[al]             \istb{B_2}[ar]            \endist
\xtdistance{15mm}{15mm}
\istroot(2a)(2-1)<135>{2}
  \istb{\alpha_2}[al]{(6,0)} \istb{\beta_2}[ar]{(3,1)} \endist
\istroot(3a)(3-1)
  \istb{\alpha_1}[al]{(3,3)} \istb{\beta_1}[ar]{(1,5)} \endist
\istroot(3b)(3-2)
  \istb{\alpha_1}[al]{(4,2)} \istb{\beta_1}[ar]{(5,1)} \endist
\xtInfoset(3a)(3b){1}
\end{istgame}

\end{document}

2. Analyze the game:

\documentclass[tikz]{standalone}
    
\usepackage{istgame}

\begin{document}

\begin{istgame}
\tikzset{KK/.style={draw=red,very thick}}

\xtdistance{10mm}{20mm}
\istroot[-45](0){2}
  \istb[KK]{C}[r]
  \istb[KK]{S}[a]{(1,2)}[b]
  \endist
\xtdistance{15mm}{60mm}
\istroot(1)(0-1)<135>{1}
  \istb[KK]{a_1}[al]
  \istb    {b_1}[ar] 
  \endist
\xtdistance{15mm}{30mm}
\istroot(2)(1-1){1}
  \istb    {A_1}[al]
  \istb[KK]{B_1}[ar]{(4,1)}
  \endist
\istroot(3)(1-2){2}
  \istb[KK]{A_2}[al]
  \istb    {B_2}[ar]
  \endist
\xtdistance{15mm}{15mm}
\istroot(2a)(2-1)<135>{2}
  \istb    {\alpha_2}[al]{(6,0)}
  \istb[KK]{\beta_2}[ar]{(3,1)}
  \endist
\istroot(3a)(3-1)
  \istb[KK]{\alpha_1}[al]{(3,3)}
  \istb    {\beta_1}[ar]{(1,5)}
  \endist
\istroot(3b)(3-2)
  \istb[KK]{\alpha_1}[al]{(4,2)}
  \istb    {\beta_1}[ar]{(5,1)}
  \endist
\xtInfoset(3a)(3b){1}
\end{istgame}

\end{document}