%%%%%%%%%%%% TODO : 
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 \title{Attracteurs}
  \author{D. CONDUCHÉ}\institute{Spé PC, Avignon}


\begin{document}
%--------------------------------------------------------------------------------------
%\begin{frame}%[label=current]
%\titlepage
%\end{frame}

%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%\section{Complément sur les séries à valeurs réelles ou complexes}%
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%



\shorthandoff{:} 
%%%%%%%%%%%%%%%%%%%%% Styles %%%%%%%%%%%%%%%%%%%%%
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}
\tikzstyle{preno}=[semithick] % arêtes non orientées.
\tikzstyle{pre}=[->,>=stealth,semithick] % arêtes orientées.
\tikzstyle{select}=[-,cap=round,style=nearly transparent,line width=6pt] %
\tikzstyle{fl_actif}=[-,cap=round,style=nearly transparent,line width=6pt,color=black!50!red]
\tikzstyle{fl_poss}=[-,cap=round,line width=2pt,color=red]
\tikzstyle{fl_obl}=[-,cap=round,line width=2pt,color=red]
\tikzstyle{fl_str}=[-,cap=round,line width=3pt,color=blue]


\tikzstyle{infini} =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!50,fill=blue!5]
\tikzstyle{encours}=[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=blue!50,fill=blue!20]
\tikzstyle{fini}   =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=black!30]
\tikzstyle{actif}  =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80!red,fill=red!20!black!30]

\tikzstyle{j1} =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!50,fill=blue!5]
\tikzstyle{j1act}=[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=blue,fill=blue!5]
\tikzstyle{j1slct}=[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=blue!50]
\tikzstyle{j1non}=[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=red,fill=blue!10]

\tikzstyle{j2}=[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!50,fill=red!5]
\tikzstyle{j2act}=[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=red,fill=red!5]
\tikzstyle{j2slct}=[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=red!50]

\tikzstyle{att0}   =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=green!20]
\tikzstyle{att1}  =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=black!10!green!60]
\tikzstyle{att2}  =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=black!25!green]
\tikzstyle{att3}  =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=black!30!green]
\tikzstyle{att4}  =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=black!35!green]
\tikzstyle{att5}  =[circle,thick,inner sep=0pt,minimum size=6mm,node distance=20mm,draw=black!80,fill=black!40!green]


\section*{Attracteurs}
\begin{frame}
Le but de cette présentation est de construire récursivement l'{\em attracteur}
pour le joueur $J_1$ sur un exemple concret : le jeu de Chomp $(2,3)$.
%\titlepage
\end{frame}
% \subsection*{Introduction}
% \begin{frame} 
% \begin{center}
% \end{center}
% \pause
% \begin{block}{}%{Exemple 1} %Exemple de CLR
% %%%%%%%%%%%%%%%%%%%%% Présentation du graphe %%%%%%%%%%%%%%%%%%%%%
% \begin{center}
% \begin{tikzpicture}[>=stealth,scale=1]
%   \node[encours,label={[red]left:A}]      (s)                            {};
%   \node[infini,label={[red]above:B}]      (t)        [above right of=s]  {};
%   \node[infini,label={[red]below:E}]      (y)        [below right of=s]  {};
%   \node[infini,label={[red]above right:C}]      (x)        [right of=t]  {};
%   \node[infini,label={[red]below right:D}]      (z)        [right of=y]  {};
% % flèches soulignées.

% % flèches et numéros
% \draw[pre] (s) to node[auto] {$10$} (t) ;
% \draw[pre] (s) to node[auto,swap] {$5$} (y) ;
% \draw[pre] (t) to node[auto] {$1$} (x) ;
% \draw[pre] (y) to node[auto,near end] {$9$} (x) ;
% \draw[pre] (y) to node[auto,swap] {$2$} (z) ;
% \draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
% \draw[pre,bend right=20] (t) to node[auto,swap] {$2$} (y) ;
% \draw[pre,bend right=20] (x) to node[auto,swap] {$4$} (z) ;
% \draw[pre,bend right=20] (z) to node[auto,swap] {$6$} (x) ;
% \draw[pre,bend left=80] (z) to node[auto] {$7$} (s) ;
% \end{tikzpicture}
% \end{center}
% \end{block}
% \end{frame}
\subsection*{Exemple : jeu de Chomp}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
%  \node[j1]   (2a)  at (0,-2)  {$2_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[j1]   (4a)  at (0,-4)  {$4_a$};
  \node[j1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[j1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
%  \node[j2]   (0b)  at (3,-0)  {$0_b$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att0]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att0, label={left:Attr $^1_0:$}]   ()  at (8,-3)  {$ $};
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}

\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_0^1$} : L'ensemble des positions finales où $J_1$
gagne. 
\pause
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
% \item $J_2$ joue et arrive forcément dans $\mathrm{Attr}_0^1$.
% \item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
% \item Pas de coups joué par $J_1$ et arrivant dans 
% $\mathrm{Attr}_0^1$.
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
%  \node[j1]   (2a)  at (0,-2)  {$2_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[j1]   (4a)  at (0,-4)  {$4_a$};
  \node[j1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[j1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
%  \node[j2]   (0b)  at (3,-0)  {$0_b$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att0]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att0, label={left:Attr $^1_0:$}]   ()  at (8,-3)  {$ $};
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_actif] (4a) to (8b) ;
  \draw[fl_actif] (5a) to (8b) ;
  \draw[fl_actif] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_0^1$} : L'ensemble des positions finales où $J_1$
gagne. 
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
% \pause
% \item $J_2$ joue et arrive dans $\mathrm{Attr}_0^1$ :
% \pause
% aucun.
% \item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
% \item Coups joués par $J_2$ arrivant dans $\mathrm{Attr}_0^1$...
\end{itemize}
\pause
\vspace{3.4cm}
{\em On sélectionne ces sommets,}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
%  \node[j1]   (2a)  at (0,-2)  {$2_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[j1slct]   (4a)  at (0,-4)  {$4_a$};
  \node[j1slct]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[j1slct]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
%  \node[j2]   (0b)  at (3,-0)  {$0_b$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att0]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att0, label={left:Attr $^1_0:$}]   ()  at (8,-3)  {$ $};
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_actif] (4a) to (8b) ;
  \draw[fl_actif] (5a) to (8b) ;
  \draw[fl_actif] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_0^1$} : L'ensemble des positions finales où $J_1$
gagne. 
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
% \pause
% \item $J_2$ joue et arrive dans $\mathrm{Attr}_0^1$ :
% \pause
% aucun.
% \item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
% \item Coups joués par $J_2$ arrivant dans $\mathrm{Attr}_0^1$...
\end{itemize}
\vspace{3.4cm}
{\em On sélectionne ces sommets,
\pause
et on note les coups de $J_1$:}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
%  \node[j1]   (2a)  at (0,-2)  {$2_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[j1slct]   (4a)  at (0,-4)  {$4_a$};
  \node[j1slct]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[j1slct]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
%  \node[j2]   (0b)  at (3,-0)  {$0_b$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att0]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att0, label={left:Attr $^1_0:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_0^1$} : L'ensemble des positions finales où $J_1$
gagne. 
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
% \pause
% \item $J_2$ joue et arrive dans $\mathrm{Attr}_0^1$ :
% \pause
% aucun sommet.
% \item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
% \item Coups joués par $J_2$ arrivant dans $\mathrm{Attr}_0^1$...
\end{itemize}
\vspace{3.4cm}
{\em On sélectionne ces sommets,
et on note les coups de $J_1$:
\pause
ce sera la stratégie de $J_1$.}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
%  \node[j1]   (2a)  at (0,-2)  {$2_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
%  \node[j2]   (0b)  at (3,-0)  {$0_b$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att0]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_0^1$} : L'ensemble des positions finales où $J_1$
gagne. 
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\pause
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
\pause
aucun sommet.
\pause
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
% \item Coups joués par $J_2$ arrivant dans $\mathrm{Attr}_0^1$...
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
%  \node[j1]   (2a)  at (0,-2)  {$2_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
%  \node[j2]   (0b)  at (3,-0)  {$0_b$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_0^1$} : L'ensemble des positions finales où $J_1$
gagne. 
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun sommet.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\pause
\underline{$\mathrm{Attr}_2^1$} : 
\pause
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
% $4_a$, $5_a$ et $7_a$.
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
% aucun.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\vspace{2cm}
\pause
{\em (Hors $8_b \in \mathrm{Attr}_0^1$ : déjà testé)}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
% $4_a$, $5_a$ et $7_a$.
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
% aucun.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\vspace{2cm}
{\em (Hors $8_b \in \mathrm{Attr}_0^1$ : déjà testé)}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\pause
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
% aucun.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}



\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2act]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (1b) to (4a) ;
%  \draw[fl_actif] (2b) to (4a) ;
  \draw[fl_actif] (1b) to (5a) ;
%  \draw[fl_actif] (2b) to (5a) ;
  % \draw[fl_actif] (3b) to (5a) ;
  % \draw[fl_actif] (6b) to (5a) ;
  % \draw[fl_actif] (3b) to (7a) ;
  % \draw[fl_actif] (4b) to (7a) ;
  % \draw[fl_actif] (6b) to (7a) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
\pause 
$1_b$ ?
% aucun.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}




\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2act]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (1b) to (4a) ;
%  \draw[fl_actif] (2b) to (4a) ;
  \draw[fl_actif] (1b) to (5a) ;
%  \draw[fl_actif] (2b) to (5a) ;
  % \draw[fl_actif] (3b) to (5a) ;
  % \draw[fl_actif] (6b) to (5a) ;
  % \draw[fl_actif] (3b) to (7a) ;
  % \draw[fl_actif] (4b) to (7a) ;
  % \draw[fl_actif] (6b) to (7a) ;
  \draw[fl_obl] (1b) to (4a) ;
  \draw[fl_obl] (1b) to (5a) ;
  \draw[fl_obl] (1b) to (6a) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$1_b$ ?\\
\pause
Non, depuis $1_b$, $J_2$ peut aller en $6_a$.
% aucun.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}



\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1non]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2act]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (1b) to (4a) ;
%  \draw[fl_actif] (2b) to (4a) ;
  \draw[fl_actif] (1b) to (5a) ;
%  \draw[fl_actif] (2b) to (5a) ;
  % \draw[fl_actif] (3b) to (5a) ;
  % \draw[fl_actif] (6b) to (5a) ;
  % \draw[fl_actif] (3b) to (7a) ;
  % \draw[fl_actif] (4b) to (7a) ;
  % \draw[fl_actif] (6b) to (7a) ;
  \draw[fl_obl] (1b) to (4a) ;
  \draw[fl_obl] (1b) to (5a) ;
  \draw[fl_obl] (1b) to (6a) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$1_b$ ?\\
Non, depuis $1_b$, $J_2$ peut aller en $6_a$.
\pause
Donc pas $1_b$.\hspace{-1cm}~
% \makebox[0pt]{$1_b$.}
% aucun.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2act]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (2b) to (4a) ;
  \draw[fl_actif] (2b) to (5a) ;
  % \draw[fl_actif] (3b) to (5a) ;
  % \draw[fl_actif] (6b) to (5a) ;
  % \draw[fl_actif] (3b) to (7a) ;
  % \draw[fl_actif] (4b) to (7a) ;
  % \draw[fl_actif] (6b) to (7a) ;
\end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
\pause
$2_b$ ?\\
% Non, depuis $1_b$, $J_2$ peut aller en $6_a$.
% \pause
% Donc pas $1_b$.\hspace{-1cm}~
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}



\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1non]   (1a)  at (0,-1)  {$1_a$};
  \node[j1non]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2act]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (2b) to (4a) ;
  \draw[fl_actif] (2b) to (5a) ;
  % \draw[fl_actif] (3b) to (5a) ;
  % \draw[fl_actif] (6b) to (5a) ;
  % \draw[fl_actif] (3b) to (7a) ;
  % \draw[fl_actif] (4b) to (7a) ;
  % \draw[fl_actif] (6b) to (7a) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (4a) ;
  \draw[fl_obl] (2b) to (5a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$2_b$ ?\\
\pause
Non.
% Non, depuis $1_b$, $J_2$ peut aller en $6_a$.
% \pause
% Donc pas $1_b$.\hspace{-1cm}~
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2act]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (3b) to (5a) ;
%  \draw[fl_actif] (6b) to (5a) ;
  \draw[fl_actif] (3b) to (7a) ;
  % \draw[fl_actif] (4b) to (7a) ;
  % \draw[fl_actif] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
\pause
$3_b$ ?\\
% \pause
% Non.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1non]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2act]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (3b) to (5a) ;
%  \draw[fl_actif] (6b) to (5a) ;
  \draw[fl_actif] (3b) to (7a) ;
  % \draw[fl_actif] (4b) to (7a) ;
  % \draw[fl_actif] (6b) to (7a) ;
  \draw[fl_obl] (3b) to (5a) ;
  \draw[fl_obl] (3b) to (6a) ;
  \draw[fl_obl] (3b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$3_b$ ?\\
\pause
Non.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1non]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2act]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
%  \draw[fl_actif] (6b) to (5a) ;
  \draw[fl_actif] (4b) to (7a) ;
  \draw[fl_obl] (4b) to (8a) ;
%  \draw[fl_actif] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$4_b$ ?\\
\pause
Non.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2act]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (6b) to (5a) ;
  \draw[fl_actif] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$ ?\\
% \pause
% Oui.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2act]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (6b) to (5a) ;
  \draw[fl_actif] (6b) to (7a) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$ ?\\
\pause
Oui.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[j2slct]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att1, label={left:Attr $^1_1:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_actif] (6b) to (5a) ;
  \draw[fl_actif] (6b) to (7a) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att1]   (4a)  at (0,-4)  {$4_a$};
  \node[att1]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att1]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att1]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att2, label={left:Attr $^1_2:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
\pause
\item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att2]   (4a)  at (0,-4)  {$4_a$};
  \node[att2]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att2]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att2]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att2, label={left:Attr $^1_2:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_1^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_0^1$ :
$4_a$, $5_a$ et $7_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_0^1$ :
aucun.
\item $\mathrm{Attr}_0^1 \subset \mathrm{Attr}_1^1$
\end{itemize}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
\item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1]   (1a)  at (0,-1)  {$1_a$};
  \node[j1]   (3a)  at (0,-3)  {$3_a$};
  \node[att2]   (4a)  at (0,-4)  {$4_a$};
  \node[att2]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att2]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att2]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att2, label={left:Attr $^1_2:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
\item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\pause
\underline{$\mathrm{Attr}_3^1$} : 
\pause
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
% aucun.
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
% \item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1slct]   (1a)  at (0,-1)  {$1_a$};
  \node[j1slct]   (3a)  at (0,-3)  {$3_a$};
  \node[att2]   (4a)  at (0,-4)  {$4_a$};
  \node[att2]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att2]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att2]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att2, label={left:Attr $^1_2:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_actif] (1a) to (6b) ;
  \draw[fl_actif] (3a) to (6b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
\item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
\pause
$1_a$ et $3_a$,
\pause
et on note la stratégie de $J_1$.
% aucun.
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
% \item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1slct]   (1a)  at (0,-1)  {$1_a$};
  \node[j1slct]   (3a)  at (0,-3)  {$3_a$};
  \node[att2]   (4a)  at (0,-4)  {$4_a$};
  \node[att2]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att2]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att2]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att2, label={left:Attr $^1_2:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_actif] (1a) to (6b) ;
  \draw[fl_actif] (3a) to (6b) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
\item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$1_a$ et $3_a$,
et on note la stratégie de $J_1$.
% aucun.
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
% \item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[j1slct]   (1a)  at (0,-1)  {$1_a$};
  \node[j1slct]   (3a)  at (0,-3)  {$3_a$};
  \node[att2]   (4a)  at (0,-4)  {$4_a$};
  \node[att2]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att2]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att2]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att2]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att2, label={left:Attr $^1_2:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
\item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$1_a$ et $3_a$,
et on note la stratégie de $J_1$.
\pause
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
\pause
aucun.
\pause
\item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\end{columns}
\end{frame}

% \begin{frame} 
% \begin{columns}
% \column[T]{0.5\linewidth}
% %%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
% \begin{tikzpicture}[>=stealth,scale=1]
%   \node[j1]   (0a)  at (0,-0)  {$0_a$};
%   \node[j1slct]   (1a)  at (0,-1)  {$1_a$};
%   \node[j1slct]   (3a)  at (0,-3)  {$3_a$};
%   \node[att2]   (4a)  at (0,-4)  {$4_a$};
%   \node[att2]   (5a)  at (0,-5)  {$5_a$};
%   \node[j1]   (6a)  at (0,-6)  {$6_a$};
%   \node[att2]   (7a)  at (0,-7)  {$7_a$};
%   \node[j1]   (8a)  at (0,-8)  {$8_a$};
%   \node[j2]   (1b)  at (3,-1)  {$1_b$};
%   \node[j2]   (2b)  at (3,-2)  {$2_b$};
%   \node[j2]   (3b)  at (3,-3)  {$3_b$};
%   \node[j2]   (4b)  at (3,-4)  {$4_b$};
%   \node[j2]   (5b)  at (3,-5)  {$5_b$};
%   \node[att2]   (6b)  at (3,-6)  {$6_b$};
%   \node[j2]   (7b)  at (3,-7)  {$7_b$};
%   \node[att2]   (8b)  at (3,-8)  {$8_b$};
% % Légende :
%   \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
%   \node[att2, label={left:Attr $^1_2:$}]   ()  at (8,-3)  {$ $};
%   \node at (6,-4) {Stratégie $J_1:$ };
%   \draw[fl_str] (7.7,-4) to (8.5,-4) ;
%   \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
%   \node at (6,-6) {Coup possible $J_2:$ };
%   \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% % flèches soulignées.
% \begin{pgfonlayer}{background}
%   \draw[fl_str] (4a) to (8b) ;
%   \draw[fl_str] (5a) to (8b) ;
%   \draw[fl_str] (7a) to (8b) ;
%   \draw[fl_obl] (6b) to (5a) ;
%   \draw[fl_obl] (6b) to (7a) ;
%   \draw[fl_str] (1a) to (6b) ;
%   \draw[fl_str] (3a) to (6b) ;
%  \end{pgfonlayer}
% % flèches et numéros
%   \draw[pre] (0a) to (1b) ;
%   \draw[pre] (0a) to (2b) ;
%   \draw[pre] (0a) to (3b) ;
%   \draw[pre] (0a) to (4b) ;
%   \draw[pre] (0a) to (5b) ;
%   \draw[pre] (1a) to (4b) ;
%   \draw[pre] (1a) to (5b) ;
%   \draw[pre] (1a) to (6b) ;
%   \draw[pre] (3a) to (5b) ;
%   \draw[pre] (3a) to (6b) ;
%   \draw[pre] (3a) to (7b) ;
%   \draw[pre] (4a) to (7b) ;
%   \draw[pre] (4a) to (8b) ;
%   \draw[pre] (5a) to (8b) ;
%   \draw[pre] (6a) to (5b) ;
%   \draw[pre] (6a) to (7b) ;
%   \draw[pre] (7a) to (8b) ;
%   \draw[pre] (1b) to (4a) ;
%   \draw[pre] (1b) to (5a) ;
%   \draw[pre] (1b) to (6a) ;
%   \draw[pre] (2b) to (1a) ;
%   \draw[pre] (2b) to (3a) ;
%   \draw[pre] (2b) to (4a) ;
%   \draw[pre] (2b) to (5a) ;
%   \draw[pre] (3b) to (5a) ;
%   \draw[pre] (3b) to (6a) ;
%   \draw[pre] (3b) to (7a) ;
%   \draw[pre] (4b) to (7a) ;
%   \draw[pre] (4b) to (8a) ;
%   \draw[pre] (5b) to (8a) ;
%   \draw[pre] (6b) to (5a) ;
%   \draw[pre] (6b) to (7a) ;
%   \draw[pre] (7b) to (8a) ;
% %\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
% \end{tikzpicture}
% \column[T]{0.3\linewidth}
% \underline{$\mathrm{Attr}_2^1$} : 
% \begin{itemize}
% \item $J_1$ joue et peut arriver dans 
% $\mathrm{Attr}_1^1$ :
% aucun.
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
% $6_b$.
% \item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
% \end{itemize}
% \underline{$\mathrm{Attr}_3^1$} : 
% \begin{itemize}
% \item $J_1$ joue et peut arriver dans 
% $\mathrm{Attr}_2^1$ :
% $1_a$ et $3_a$,
% et on note la stratégie de $J_1$.
% \pause
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
% \pause
% aucun.
% \pause
% \item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
% \end{itemize}
% \end{columns}
% \end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[att3]   (1a)  at (0,-1)  {$1_a$};
  \node[att3]   (3a)  at (0,-3)  {$3_a$};
  \node[att3]   (4a)  at (0,-4)  {$4_a$};
  \node[att3]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att3]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att3]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att3]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att3, label={left:Attr $^1_3:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_2^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_1^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_1^1$ :
$6_b$.
\item $\mathrm{Attr}_1^1 \subset \mathrm{Attr}_2^1$
\end{itemize}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$1_a$ et $3_a$,
et on note la stratégie de $J_1$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
aucun.
\item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[att3]   (1a)  at (0,-1)  {$1_a$};
  \node[att3]   (3a)  at (0,-3)  {$3_a$};
  \node[att3]   (4a)  at (0,-4)  {$4_a$};
  \node[att3]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att3]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att3]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att3]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att3, label={left:Attr $^1_3:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$1_a$ et $3_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
aucun.
\item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\pause
\underline{$\mathrm{Attr}_4^1$} : 
\pause
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_3^1$ :
\pause
aucun.
\pause
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_3^1$ :
% $6_b$.
% \item $\mathrm{Attr}_3^1 \subset \mathrm{Attr}_4^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[att3]   (1a)  at (0,-1)  {$1_a$};
  \node[att3]   (3a)  at (0,-3)  {$3_a$};
  \node[att3]   (4a)  at (0,-4)  {$4_a$};
  \node[att3]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att3]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2act]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att3]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att3]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att3, label={left:Attr $^1_3:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
  \draw[fl_actif] (2b) to (1a) ;
  \draw[fl_actif] (2b) to (3a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$1_a$ et $3_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
aucun.
\item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\underline{$\mathrm{Attr}_4^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_3^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_3^1$ :
\pause
$2_b$ ?
% \item $\mathrm{Attr}_3^1 \subset \mathrm{Attr}_4^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[att3]   (1a)  at (0,-1)  {$1_a$};
  \node[att3]   (3a)  at (0,-3)  {$3_a$};
  \node[att3]   (4a)  at (0,-4)  {$4_a$};
  \node[att3]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att3]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2act]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att3]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att3]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att3, label={left:Attr $^1_3:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
  \draw[fl_actif] (2b) to (1a) ;
  \draw[fl_actif] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (4a) ;
  \draw[fl_obl] (2b) to (5a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$1_a$ et $3_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
aucun.
\item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\underline{$\mathrm{Attr}_4^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_3^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_3^1$ :
$2_b$ ?
\pause
Oui.
% \item $\mathrm{Attr}_3^1 \subset \mathrm{Attr}_4^1$
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[att3]   (1a)  at (0,-1)  {$1_a$};
  \node[att3]   (3a)  at (0,-3)  {$3_a$};
  \node[att3]   (4a)  at (0,-4)  {$4_a$};
  \node[att3]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att3]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[j2slct]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att3]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att3]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att3, label={left:Attr $^1_3:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (4a) ;
  \draw[fl_obl] (2b) to (5a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_3^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$1_a$ et $3_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_2^1$ :
aucun.
\item $\mathrm{Attr}_2^1 \subset \mathrm{Attr}_3^1$
\end{itemize}
\underline{$\mathrm{Attr}_4^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_3^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_3^1$ :
$2_b$.
\pause
\item $\mathrm{Attr}_3^1 \subset \mathrm{Attr}_4^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1]   (0a)  at (0,-0)  {$0_a$};
  \node[att4]   (1a)  at (0,-1)  {$1_a$};
  \node[att4]   (3a)  at (0,-3)  {$3_a$};
  \node[att4]   (4a)  at (0,-4)  {$4_a$};
  \node[att4]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att4]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[att4]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att4]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att4]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att4, label={left:Attr $^1_4:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (4a) ;
  \draw[fl_obl] (2b) to (5a) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_4^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_3^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_3^1$ :
$2_b$.
\item $\mathrm{Attr}_3^1 \subset \mathrm{Attr}_4^1$
\end{itemize}
\pause
\underline{$\mathrm{Attr}_5^1$} : 
\pause
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
\pause
$0_a$.
% \item $J_2$ joue et doit arriver dans $\mathrm{Attr}_4^1$ :
% aucun.
% \item $\mathrm{Attr}_4^1 \subset \mathrm{Attr}_5^1$
\end{itemize}
\end{columns}
\end{frame}


\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[j1slct]   (0a)  at (0,-0)  {$0_a$};
  \node[att4]   (1a)  at (0,-1)  {$1_a$};
  \node[att4]   (3a)  at (0,-3)  {$3_a$};
  \node[att4]   (4a)  at (0,-4)  {$4_a$};
  \node[att4]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att4]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[att4]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att4]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att4]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att4, label={left:Attr $^1_4:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (4a) ;
  \draw[fl_obl] (2b) to (5a) ;
  \draw[fl_str] (0a) to (2b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_4^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_3^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_3^1$ :
$2_b$.
\item $\mathrm{Attr}_3^1 \subset \mathrm{Attr}_4^1$
\end{itemize}
\underline{$\mathrm{Attr}_5^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$0_a$.
\pause
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_4^1$ :
aucun.
\pause
\item $\mathrm{Attr}_4^1 \subset \mathrm{Attr}_5^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[att5]   (0a)  at (0,-0)  {$0_a$};
  \node[att5]   (1a)  at (0,-1)  {$1_a$};
  \node[att5]   (3a)  at (0,-3)  {$3_a$};
  \node[att5]   (4a)  at (0,-4)  {$4_a$};
  \node[att5]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att5]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[att5]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att5]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att5]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att5, label={left:Attr $^1_5:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (4a) ;
  \draw[fl_obl] (2b) to (5a) ;
  \draw[fl_str] (0a) to (2b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_4^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_3^1$ :
aucun.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_3^1$ :
$2_b$.
\item $\mathrm{Attr}_3^1 \subset \mathrm{Attr}_4^1$
\end{itemize}
\underline{$\mathrm{Attr}_5^1$} : 
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_2^1$ :
$0_a$.
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_4^1$ :
aucun.
\item $\mathrm{Attr}_4^1 \subset \mathrm{Attr}_5^1$
\end{itemize}
\end{columns}
\end{frame}

\begin{frame} 
\begin{columns}
\column[T]{0.5\linewidth}
%%%%%%%%%%%%%%%%%%%%% Étape 1 %%%%%%%%%%%%%%%%%%%%%
\begin{tikzpicture}[>=stealth,scale=1]
  \node[att5]   (0a)  at (0,-0)  {$0_a$};
  \node[att5]   (1a)  at (0,-1)  {$1_a$};
  \node[att5]   (3a)  at (0,-3)  {$3_a$};
  \node[att5]   (4a)  at (0,-4)  {$4_a$};
  \node[att5]   (5a)  at (0,-5)  {$5_a$};
  \node[j1]   (6a)  at (0,-6)  {$6_a$};
  \node[att5]   (7a)  at (0,-7)  {$7_a$};
  \node[j1]   (8a)  at (0,-8)  {$8_a$};
  \node[j2]   (1b)  at (3,-1)  {$1_b$};
  \node[att5]   (2b)  at (3,-2)  {$2_b$};
  \node[j2]   (3b)  at (3,-3)  {$3_b$};
  \node[j2]   (4b)  at (3,-4)  {$4_b$};
  \node[j2]   (5b)  at (3,-5)  {$5_b$};
  \node[att5]   (6b)  at (3,-6)  {$6_b$};
  \node[j2]   (7b)  at (3,-7)  {$7_b$};
  \node[att5]   (8b)  at (3,-8)  {$8_b$};
% Légende :
  \node[j1, label={left:Joueur $1:$}]   ()  at (8,-2)  {$ $};
  \node[att5, label={left:Attr $^1_5:$}]   ()  at (8,-3)  {$ $};
  \node at (6,-4) {Stratégie $J_1:$ };
  \draw[fl_str] (7.7,-4) to (8.5,-4) ;
  \node[j2, label={left:Joueur $2:$}]   ()  at (8,-5)  {$ $};
  \node at (6,-6) {Coup possible $J_2:$ };
  \draw[fl_obl] (7.7,-6) to (8.5,-6) ;
% flèches soulignées.
\begin{pgfonlayer}{background}
  \draw[fl_str] (4a) to (8b) ;
  \draw[fl_str] (5a) to (8b) ;
  \draw[fl_str] (7a) to (8b) ;
  \draw[fl_obl] (6b) to (5a) ;
  \draw[fl_obl] (6b) to (7a) ;
  \draw[fl_str] (1a) to (6b) ;
  \draw[fl_str] (3a) to (6b) ;
  \draw[fl_obl] (2b) to (1a) ;
  \draw[fl_obl] (2b) to (3a) ;
  \draw[fl_obl] (2b) to (4a) ;
  \draw[fl_obl] (2b) to (5a) ;
  \draw[fl_str] (0a) to (2b) ;
 \end{pgfonlayer}
% flèches et numéros
  \draw[pre] (0a) to (1b) ;
  \draw[pre] (0a) to (2b) ;
  \draw[pre] (0a) to (3b) ;
  \draw[pre] (0a) to (4b) ;
  \draw[pre] (0a) to (5b) ;
  \draw[pre] (1a) to (4b) ;
  \draw[pre] (1a) to (5b) ;
  \draw[pre] (1a) to (6b) ;
  \draw[pre] (3a) to (5b) ;
  \draw[pre] (3a) to (6b) ;
  \draw[pre] (3a) to (7b) ;
  \draw[pre] (4a) to (7b) ;
  \draw[pre] (4a) to (8b) ;
  \draw[pre] (5a) to (8b) ;
  \draw[pre] (6a) to (5b) ;
  \draw[pre] (6a) to (7b) ;
  \draw[pre] (7a) to (8b) ;
  \draw[pre] (1b) to (4a) ;
  \draw[pre] (1b) to (5a) ;
  \draw[pre] (1b) to (6a) ;
  \draw[pre] (2b) to (1a) ;
  \draw[pre] (2b) to (3a) ;
  \draw[pre] (2b) to (4a) ;
  \draw[pre] (2b) to (5a) ;
  \draw[pre] (3b) to (5a) ;
  \draw[pre] (3b) to (6a) ;
  \draw[pre] (3b) to (7a) ;
  \draw[pre] (4b) to (7a) ;
  \draw[pre] (4b) to (8a) ;
  \draw[pre] (5b) to (8a) ;
  \draw[pre] (6b) to (5a) ;
  \draw[pre] (6b) to (7a) ;
  \draw[pre] (7b) to (8a) ;
%\draw[pre,bend right=20] (y) to node[auto,swap] {$3$} (t) ;
\end{tikzpicture}
\column[T]{0.3\linewidth}
\underline{$\mathrm{Attr}_6^1$} : 
\pause
\begin{itemize}
\item $J_1$ joue et peut arriver dans 
$\mathrm{Attr}_5^1$ :
\pause
aucun.
\pause
\item $J_2$ joue et doit arriver dans $\mathrm{Attr}_5^1$ :
\pause
aucun.
\pause
\item $\mathrm{Attr}_5^1 \subset \mathrm{Attr}_6^1$
\end{itemize}
\pause
Donc $\mathrm{Attr}_6^1 = \mathrm{Attr}_5^1$\\
\pause
De même, 
\pause
pour tout $i\geq 6$,
\pause
$$\mathrm{Attr}_i^1 = \mathrm{Attr}_5^1$$
\pause
\bigskip
Conclusion :
\pause
\[\hspace{-3cm}\mathrm{Attr}^1 = 
\bigcup_{i\in \N}\mathrm{Attr}_i^1 
= \{0_a, 1_a, 2_b, 3_a, 4_a, 5_a, 6_b, 7_a, 8_b\}\]



\end{columns}
\end{frame}






\end{document}
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