%&latex
\documentclass[12pt]{article}
\usepackage{url}
\usepackage{egame}


\begin{document}

\begin{center}
\textbf{An example by Fioravante Patrone (\url{<patrone@dima.unige.it>})}
\end{center}

Few initial comments:\\
This game tree presented some difficulties:\\
- a careful choice for spacing was needed. Some preliminary calculations were indeed useful: notice that there are many branches and that the spacing between nodes lying at the same ``level'' is uneven. The goal was to get a good final distribution of spacing among the terminal nodes. See below for details\\
- the description of the game is divided into ``levels'' (its meaning should be self-explanatory, having seen the Figure)\\
- not all of the labels for branches were written: this choice was made to improve readability\\
- further comments, specific to some tricks used, are in ``commented'' lines
\newline\\
- spacing details:\\
I had to put 16 nodes at the last level. So, I decided a spacing among them of 80 units (each unit is 0.1 mm).\\
From this came the horizontal space allotted for the figure: 1600 units\\
For vertical spacing, I left 160 units between any two levels. Since the levels are 5 (4 have decision nodes, the 5th has the outcomes), this amounts to 800, so I left 880 units for the overall vertical size of the figure\\
Here are the horizontal coordinates of the various levels:\\
4th level: 80, 160, 280, 400, 480, 600, 720, 800, 880, 960, 1080, 1240\\
3rd level: 80, 160, 280, 400, 480, 600, 760, 920, 1160\\
2nd level: 160, 480, 960\\
1st level: 480 (the initial node was put there, that is a little to left w.r.t.\ center of the figure, for aesthetical reasons but also to comply with the restrictions that the macro by Osborne puts on the horizontal vs.\ vertical ratio)\\

%% \vphantom's added by Martin J. Osborne to make the baselines of 
%% all outcomes align.

\begin{figure}[htb]
\hspace*{\fill}
\begin{egame}(1600,880)

%%%%
%%%% first level
%%%%

\putbranch(480,800)(-2,1){320}
\ib{$1$}[l]{$\{t\}$}

%%% A TRICK
%%% this is the way I found to get 
%%% printed the branch label.
%%% This ``commented'' way (should be the plain one) did not work
%\putbranch(480,800)(0,1){160}
%\ib{}[r]{$\{b\}$}

\putbranch(480,800)(0,-1)[l]{160}
\ib{}{$\{b\}$}

\putbranch(480,800)(3,1){480}
\ib{}[r]{$\{t,b\}$}

%%%%
%%%% second level
%%%%

% to reduce spacing for the labels. A standard well documented feature
\egactionlabelsep=0.1mm

%%%% left hand part
\putbranch(160,640)(-1,2){80}
\ib{}[l]{$\{l\}$}

\putbranch(160,640)(0,1){160}
\ib{}{$\{r\}$}

\putbranch(160,640)(3,4){120}
\ib{}[r]{$\{l,r\}$}

%%%% central part

\putbranch(480,640)(-1,2){80}
\ib{}[l]{$\{l\}$}

\putbranch(480,640)(0,1){160}
\ib{}{$\{r\}$}

\putbranch(480,640)(3,4){120}
\ib{}[r]{$\{l,r\}$}

%%%% right hand part

\putbranch(960,640)(-5,4){200}
\ib{}[l]{$\{l\}$}

%%% A TRICK
%%% this is the way I found to avoid
%%% that the branch label gets printed over a branch
%%% This ``commented'' way (should be the plain one) gave this kind of problem
%\putbranch(960,640)(-1,4){40}
%\ib{}[r]{$\{r\}$}

\putbranch(960,640)(-1,-4)[l]{40}
\ib{}{$\{r\}$}

\putbranch(960,640)(5,4){200}
\ib{}[r]{$\{l,r\}$}

\infoset(160,640){800}{2}


%%%%
%%%% third level
%%%%

\egactionlabelsep=0.7mm

%%%% left hand part

%%% A TRICK
%%% this is the way I found to get printed the label for the branch ...
\putbranch(80,480)(0,-1)[r]{160}
\ib{}{$t$}

%%% ... and also the player label (notic the very short branch)
%%% I used this and not the previous, to get the standard
%%% position for the player's label
\putbranch(80,480)(0,1){1}
\ib{1\ \ }{}

%%% This ``commented'' way (should be the plain one) did not give the result wanted:
%%% the label for the branch is not printed
%\putbranch(80,480)(0,1){160}
%\ib{1}[l]{$t$}



% here, as in many other places, blanks have been added for better 
% positioning the player's label
\putbranch(160,480)(0,1){160}
\ib{\ \ 1}{$t$}

\putbranch(280,480)(0,1){160}
\ib{1}[r]{$t$}


%%%% central part

\putbranch(400,480)(0,1){160}
\ib{1}[l]{$t$}

\putbranch(480,480)(0,1){160}
\ib{\ \ 1}{$t$}

\putbranch(600,480)(0,1){160}
\ib{1}[r]{$t$}

%%%% right hand part

\putbranch(760,480)(1,4){40}
\iib{1}[l]{$t$}{$b$}

\putbranch(920,480)(1,4){40}
\iib{1}[l]{$t$}{$b$}

\putbranch(1160,480)(1,2){80}
\iib{1}[r]{$t$}{$b$}

%%%%
%%%% third level
%%%%

%%%% left hand part

%%% A TRICK already used! To print as I want the labels for branch and player 

\putbranch(80,320)(0,-1)[r]{160}
\ib{}{$l$}[$\vphantom{d}a$]
\putbranch(80,320)(0,1){1}
\ib{2\ \ \ }{}

\putbranch(160,320)(0,1){160}
\ib{\ \ 2}{$r$}[$b$]

\putbranch(280,320)(1,4){40}
\iib{\ \ 2}{$l$}{$r$}[$\vphantom{d}a$][$b$]

%%%% central part

\putbranch(400,320)(0,1){160}
\ib{2}[l]{$l$}[$\vphantom{d}c$]

\putbranch(480,320)(0,1){160}
\ib{\ \ 2}{$\vphantom{d}r$}[$d$]

\putbranch(600,320)(1,4){40}
\iib{\ \ 2}{$l$}{$r$}[$\vphantom{d}c$][$d$]


%%%% right hand part
%%%% sub-left part

\putbranch(720,320)(0,1){160}
\ib{}[l]{$l$}[$\vphantom{d}a$]

\putbranch(800,320)(0,1){160}
\ib{}{$r$}[$\vphantom{d}c$]

\infoset(720,320){80}{2}


\putbranch(880,320)(0,1){160}
\ib{}{$l$}[$b$]

\putbranch(960,320)(0,1){160}
\ib{}{$l$}[$d$]

\infoset(880,320){80}{2}


%%%% right hand part
%%%% sub-right part

\putbranch(1080,320)(1,4){40}
\iib{}{$l$}{$r$}[$\vphantom{b}a$][$b$]

\putbranch(1240,320)(1,4){40}
\iib{}{$l$}{$r$}[$\vphantom{d}c$][$d$]

\infoset(1080,320){160}{2}

\end{egame}
\hspace*{\fill}
\caption[]{An example from F. Patrone, used for a joint paper with Garcia-Jurado and Mendez-Naya}\label{extensiveUC}
\end{figure}



\end{document}

