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\begin{tikzpicture}[
  scale=.9, transform shape,
  grow=right,
  sloped,
  level distance=3cm,
  level 1/.style={sibling distance=6cm},
  level 2/.style={sibling distance=4cm},
  level 3/.style={sibling distance=2cm},
  level 4/.style={sibling distance=2cm, font=\footnotesize},
  edge from parent/.style={draw, font=\footnotesize},
  auto
]

\documentclass[12pt,a4paper,onecolumn,oneside]{article}
\usepackage[ngerman]{babel}
\usepackage[T1]{fontenc}
\usepackage{lmodern}                     
\usepackage{amsmath}
\usepackage{amsfonts}
\usepackage{amssymb}
\usepackage{float}
\usepackage{amsthm}
\usepackage{multirow,array}
%\usepackage{fourier}
\usepackage{ragged2e}
\usepackage{caption}
\usepackage{tikz}
\usetikzlibrary{trees}
\usepackage{verbatim}
\captionsetup{format=plain,font=small,labelfont=bf,labelsep=colon,justification=RaggedRight}
\captionsetup[figure]{labelfont={bf},labelformat={default},labelsep=period,name={Fig.}}
\usepackage{color}
\usepackage{transparent}
\usepackage{calligra}
\usepackage[left=3cm,right=2cm,top=2cm,bottom=2cm]{geometry}

%\emergencystretch=\maxdimen
%\hyphenpenalty=10000


\begin{document}
\begin{figure}[H]
\begin{center}
\begin{tikzpicture}[
  grow=right,
  sloped,
  level distance=3cm,
  level 1/.style={sibling distance=6cm},
  level 2/.style={sibling distance=4cm},
  level 3/.style={sibling distance=2cm},
  level 4/.style={sibling distance=2cm, font=\footnotesize},
  edge from parent/.style={draw, font=\footnotesize},
  auto
]
  %1. Haupt Knoten 2.Child Knoten 3. Child Knoten 
\node{B}
  child {node {S}% Oben
    child {node {$\binom{v-p_0(k)-k}{p_0(k)+k-c}$}
      edge from parent node [auto=right]{$d=1$}
    }
    child {node {B} 
      child{node {S}
        child{node {$\binom{-p_0(k)}{p_0(k)}$}
          edge from parent node [auto=right] {$d=1$}% <- d=1
        }
        child{node {$\binom{v-p_0(k)-c}{p_0(k)}$}
          edge from parent node {$d=0$}% <- d=0
        }
        edge from parent node {$(p_0(k),c)$}
      }
      edge from parent node {$d=0$ }
    }
    edge from parent node [auto=right] {$(p_0(k),k)$; $k<c$}
  }
  child {node {S}
    child {node {$\binom{v-p_0(c)-c}{p_0(c)}$}
      edge from parent node [auto=right]  {$d=1$}
    }
    child {node {$\binom{-p_o(c)}{p_0(c)}$}
      edge from parent node {$d=0$}
    }
    edge from parent node {$(p_0(c),c)$; $k=c$}
  };
\end{tikzpicture}
\end{center}
\caption{Gleichgewicht im Fall a)}
\end{figure}
\end{document}