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diff --git a/Master/texmf-dist/doc/latex/sgame/sgame.tex b/Master/texmf-dist/doc/latex/sgame/sgame.tex new file mode 100644 index 00000000000..dfed299276a --- /dev/null +++ b/Master/texmf-dist/doc/latex/sgame/sgame.tex @@ -0,0 +1,524 @@ +% +% +% +\documentclass[12pt]{article} +\usepackage{mjoarti} +\usepackage{mathpazo} +\usepackage{pstricks} +\usepackage{pstcol,pst-mjo} +\usepackage{sgame} +\usepackage{url} +\begin{document} + +\renewcommand{\descriptionlabel}[1]{\hspace\labelsep + \normalfont #1\phantom{.}} + +\begin{center} +{\bfseries Manual for {\tt sgame.sty} and {\tt sgamevar.sty}}\\ +by\\ +Martin J. Osborne\\ +{\tt Martin.Osborne@utoronto.ca}\\ +For Version 2.13, 2005/7/8 +\end{center} + +{\sloppy +\section{Introduction} +{\tt sgame.sty} and {\tt sgamevar.sty} are \LaTeXe\ style files for drawing +strategic games. The latest versions are available at +\url{http://www.economics.utoronto.ca/osborne/latex}. The styles are +incompatible with \texttt{array.sty} (and hence any package, like +\texttt{jurabib.sty}, that loads \texttt{array.sty}). Please notify me of +bugs. +\section{sgame.sty versus sgamevar.sty} +\verb+sgame.sty+ and \verb+sgamevar.sty+ differ in two respects. +\begin{itemize} + \item The character that ``tabs'' to a new column is \verb+&+ in +\verb+sgame.sty+ and \verb+\>+ in \verb+sgamevar.sty+. In every other respect +the syntax is identical. This manual applies to \verb+sgame.sty+. If you are +using \verb+sgamevar.sty+, replace every occurrence of \verb+&+ with +\verb+\>+. + \item \verb+sgame.sty+ produces a \verb+game+ environment that cannot be +used as an argument of a macro, whereas \verb+sgamevar.sty+ does not have this +limitation. You need to use \verb+sgamevar.sty+, for example, to be able to +make a \verb+game+ environment an argument of TeXPower's \verb+\stepwise+ +macro. +\end{itemize} + +(I prefer the \verb+&+ syntax, but have been unable to find a way of +implementing it without changing the \verb+\catcode+ of \verb+&+, which +prevents a \verb+game+ environment from being the argument of a macro.) +\section{Installation} +\begin{itemize} + \item Put \texttt{sgame.sty} (and/or \texttt{sgamevar.sty}) in a directory +from which \TeX\ reads input files. (In MiKTeX the directory might be +something like \verb+\miktex\localtexmf\tex\latex\+ or a subdirectory +thereof.) + \item Let \TeX\ know that \texttt{sgame} and/or \texttt{sgamevar} have +arrived. (In MiKTeX, ``refresh the filename database''.) + \item Check that you have the \verb+color+ package. One way to check is to +put \verb+\usepackage{color}+ in the preamble of a document and see if you get +an error. If you don't have the package, get it from CTAN. + \item To use the package in a document, put the lines +\verb+\usepackage{sgame}+ (or \verb+\usepackage{sgamevar}+) and +\verb+\usepackage{color}+ (or \verb+\usepackage{pstcol}+, part of PSTricks, +which loads \verb+color+) in the preamble. + \item The style is incompatible with \verb+colortbl.sty+. +\end{itemize} +\section{Description} +The style defines two environments, \verb+game+ and \verb+game*+. Each +environment can be used in four ways, depending on the values of its optional +arguments. In each case, the starred version differs from the unstarred +versionin that action labels are not accommodated. +\subsection{No optional argument} +Without any optional arguments, its syntax is\vspace*{4mm}\newline +\verb+\begin{game}{+\emph{number-of-rows}% +\verb+}{+\emph{number-of-columns}\verb+}+\emph{game-body}% +\verb+\end{game}+\vspace*{4mm}\newline +where \emph{number-of-rows} is the number of rows in the game and +\emph{number-of-columns} is the number of columns. \emph{game-body} consists +of rows in the style of the rows in a \verb+tabular+ environment, \verb+&+ +``tabbing'' to a new cell, and \verb+\\+ ending a row. + +The following example is illustrated in Figure~\ref{f:ex1}. + +\begin{verbatim} +\def\sgtextcolor{blue}% +\def\sglinecolor{red}% +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{2} + & $L$ & $R$\\ +$T$ &$2,2$ &$100,35$\\ +$B$ &$3,0$ &$350,16$ +\end{game}\hspace*{\fill}% +\begin{game*}{2}{2} +$2,2$ &$100,35$\\ +$3,0$ &$350,16$ +\end{game*}\hspace*{\fill}% +\caption[]{A two row, two column strategic game, with and without +action labels.} +\end{figure} +\end{verbatim} + +\def\sgtextcolor{blue}% +\def\sglinecolor{red}% +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$2,2$&$100,35$\\ +$B$&$3,0$&$350,16$ +\end{game}\hspace*{\fill}% +\begin{game*}{2}{2} +$2,2$&$100,35$\\ +$3,0$&$350,16$ +\end{game*}\hspace*{\fill}% +\caption[]{A two row, two column strategic game, with and without action +labels.}\label{f:ex1} +\end{figure} +\begin{itemize} + \item Note that the width of every column is the same. Further, the +content of each cell of the table is centered vertically. + \item As in a \LaTeXe\ \verb+tabular+ environment, spaces on either side of +the text in each cell is ignored. (Thus in the \verb+tex+ file you can, if +you wish, align the columns using spaces or tabs.) + \item The first \verb+&+ {\bfseries must} be preceded by a space token +(space or carriage return). (It may not immediately follow the closing brace +of the second argument.) + \item If all the text in every cell of the payoff matrix is in math mode, +you can avoid typing all the \verb+$+'s by setting \verb+\gamemathtrue+, +either by putting this command in your file, or by changing +\verb+\gamemathfalse+ to \verb+\gamemathtrue+ in the style file. Under this +setting, all text in every cell of the payoff matrix is automatically in math +mode. (Note that even if the text in the cells consists only of +comma-separated pairs of numbers, it should still be in math mode, else the +spacing is not correct.) +\end{itemize} +\subsection{One optional argument: game label} +With one optional argument, the syntax of the \verb+game+ environment +is\vspace*{4mm}\newline +\verb+\begin{game}{+\emph{number-of-rows}% +\verb+}{+\emph{number-of-columns}\verb+}[+\emph{game-label}% +\verb+]+\emph{game-body}\newline\verb+\end{game}+\vspace*{4mm}\newline +where \emph{number-of-rows} is the number of rows in the game, +\emph{number-of-columns} is the number of columns, and \emph{game-label} is a +label for the game that is centered beneath the game. (The sense in which it +is centered may be changed by setting \verb+\irpawcgltrue+ or +\verb+\irplwcgltrue+---see Section~\ref{s:param}.) This case is useful if two +or more games are positioned side-by-side, and each requires a label. + +The following example is illustrative. + +\begin{verbatim} +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{2}[$A$] + & $L$ & $R$\\ +$a$ &$2,2$ &$0,3$\\ +$b$ &$3,0$ &$1,1$ +\end{game}\hspace*{20mm}% +\begin{game}{2}{2}[$B$] + & $L$ & $R$\\ +$a$ &$2,3$ &$0,4$\\ +$b$ &$3,1$ &$1,2$ +\end{game}\hspace*{\fill}% +\caption[]{A three player strategic game, in which +player~3 chooses $A$ or $B$.} +\end{figure} +\end{verbatim} + +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{2}[$A$] + & $L$ & $R$\\ +$a$ &$2,2$ &$0,3$\\ +$b$ &$3,0$ &$1,1$ +\end{game}\hspace*{20mm}% +\begin{game}{2}{2}[$B$] + & $L$ & $R$\\ +$a$ &$2,3$ &$0,4$\\ +$b$ &$3,1$ &$1,2$ +\end{game}\hspace*{\fill}% +\caption[]{A three player strategic game, in which player~3 chooses $A$ or +$B$.}\label{f:ex2} +\end{figure} +\subsection{Two optional arguments: player labels} +In the case of two optional arguments, the syntax of the \verb+game+ +environment is\vspace*{4mm}\newline +\verb+\begin{game}{+\emph{number-of-rows}% +\verb+}{+\emph{number-of-columns}\verb+}[+\emph{row-player-label}% +\verb+]+\newline +\verb+[+\emph{column-player-label}% +\verb+]+\emph{game-body}\verb+\end{game}+\vspace*{4mm}\newline +where \emph{number-of-rows} is the number of rows in the game, +\emph{number-of-columns} is the number of columns, and \emph{row-player-label} +and \emph{column-player-label} are the names of the players. + +The following example illustrates this case. + +\begin{verbatim} +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{3}[Player~1][Player~2] + & $L$ & $M$ & $R$\\ +$T$ &$2,2$ &$2,0$ &$0,3$\\ +$B$ &$3,0$ &$0,9$ &$1,1$ +\end{game}\hspace*{\fill}% +\caption[]{A two row, three column strategic game with +player labels.} +\end{figure} +\end{verbatim} + +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{3}[Player~1][Player~2] +&$L$&$M$&$R$\\ +$T$&$2,2$&$2,0$&$0,3$\\ +$B$&$3,0$&$0,9$&$1,1$ +\end{game}\hspace*{\fill}% +\caption[]{A two row, three column strategic game with player +labels.}\label{f:ex3} +\end{figure} +\subsection{Three optional arguments: player labels and game label} +The case of three optional arguments combines the two previous cases: the +syntax of the \verb+game+ environment is\vspace*{4mm}\newline +\verb+\begin{game}{+\emph{number-of-rows}% +\verb+}{+\emph{number-of-columns}\verb+}[+\emph{row-player-label}% +\verb+]+\newline +\verb+[+\emph{column-player-label}% +\verb+][+\emph{game-label}\verb+]+\emph{game-body}\verb+\end{game}+\vspace*{4m% +m}\newline +where \emph{number-of-rows} is the number of rows in the game, +\emph{number-of-columns} is the number of columns, \emph{row-player-label} and +\emph{column-player-label} are the names of the players, and \emph{game-label} +is a label for the game. + +The following example illustrates this case. + +\begin{verbatim} +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{3}[Player~1][Player~2][$A$] + & $L$ & $M$ & $R$\\ +$T$ &$2,2$ &$2,0$ &$0,3$\\ +$B$ &$3,0$ &$0,9$ &$1,1$ +\end{game}\hspace*{\fill}% +\caption[]{A two row, three column strategic game with +player labels and a label.} +\end{figure} +\end{verbatim} + +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{3}[Player~1][Player~2][$A$] +&$L$&$M$&$R$\\ +$T$&$2,2$&$2,0$&$0,3$\\ +$B$&$3,0$&$0,9$&$1,1$ +\end{game}\hspace*{\fill}% +\caption[]{A two row, three column strategic game with player labels and a +label.}\label{f:ex4} +\end{figure} +\section{Cell formatting} +You may regard the format of the payoffs in the first column of the game in +Figure~\ref{f:ex5} as unsatisfactory, and the formatting in the left panel of +Figure~\ref{f:ex6} as superior. This latter formatting is implemented by +adding ``phantom'' minus signs before the ``2'' in the top left cell and +before the ``3'' in the bottom left cell. The top left cell, for example, is +entered as \verb+$-2,\phantom{-}2$+. (\verb+\phantom{<x>}+ leaves a space +whose size is equal to the size of the object \verb+<x>+.) +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$-2,2$&$0,3$\\ +$B$&$3,-4$&$1,1$ +\end{game}\hspace*{\fill}% +\caption[]{A strategic game.}\label{f:ex5} +\end{figure} + +You may want to consider other formats. The right panel of Figure~\ref{f:ex6} +shows an alternative. This format is achieved be entering the element of each +cell as +\begin{quote} +\verb+\begin{array}{c}#1\\[1.6mm]#2\end{array}+, +\end{quote} +where \verb+#1+ is player~1's payoff and \verb+#2+ is player~2's payoff. +(Actually, I defined the macro +\begin{quotation} +\verb+\def\stackedpayoffs#1#2{%+ + +\verb+ \begin{array}{c}#1\\[1.6mm]#2\end{array}+ + +\verb+}+ +\end{quotation} +and entered each element as \verb+\stackedpayoffs{#1}{#2}+. I set +\verb+\gamestretch+ to be 2.1 to improve the appearance of the game.)% +\def\stackedpayoffs#1#2{\begin{array}{c}#1\\[1.6mm]#2\end{array}} +\begin{figure}[htb]\hspace*{\fill}% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$-2,\phantom{-}2$&$0,3$\\ +$B$&$\phantom{-}3,-4$&$1,1$ +\end{game}\hspace*{\fill}% +\renewcommand{\gamestretch}{2.1}% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$\stackedpayoffs{-2}{2}$&$\stackedpayoffs{0}{3}$\\ +$B$&$\stackedpayoffs{3}{-4}$&$\stackedpayoffs{1}{1}$ +\end{game}\hspace*{\fill}% +\caption[]{Two alternative presentations of the game in +Figure~\protect\ref{f:ex5}.}\label{f:ex6} +\end{figure} + +Figure~\ref{f:ex7} shows two more alternatives. The one on the left is +achieved by entering the element of each cell as +\begin{quote} +\verb+\begin{array}{rl}#1&\\[1.6mm]\end{array}+, +\end{quote} +and the one on the left differs only in that there is a \verb+\phantom{-}+ in +front of player~2's payoff in the top left cell, player~1's payoff in the +bottom left cell, and player~2's payoffs in both of the right cells.% +\def\binmorepayoffs#1#2{\begin{array}{rl}#1&\\[1.6mm]\end{array}} +\begin{figure}[htb]\hspace*{\fill}% +\renewcommand{\gamestretch}{2.1}% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$\binmorepayoffs{-2}{2}$&$\binmorepayoffs{0}{3}$\\ +$B$&$\binmorepayoffs{3}{-4}$&$\binmorepayoffs{1}{1}$ +\end{game}\hspace*{\fill}% + +\vspace*{4mm} + +\hspace*{\fill}% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$\binmorepayoffs{-2}{\phantom{-}2}$& $\binmorepayoffs{0}{\phantom{-}3}$\\ +$B$&$\binmorepayoffs{\phantom{-}3}{-4}$& $\binmorepayoffs{1}{\phantom{-}1}$ +\end{game}\hspace*{\fill}% +\caption[]{Two additional presentations of the game in +Figure~\protect\ref{f:ex5}.}\label{f:ex7} +\end{figure} +\section{Vertical position of text within cells}\label{s:VertPos} +The vertical distance between the lines at the top and bottom of a row in +\LaTeX's \verb+tabular+ environment is equal to \verb+\arraystretch+ times +\verb+\baselineskip+. The baseline of the text in each cell is placed 30\% of +the distance from the bottom line. Thus if \verb+\arraystretch+ is large +relative to the height of the text, the text is not near the middle of the +row. (See the left panel of Figure~\ref{f:VertPos}; or try setting +\verb+\arraystretch+ equal to 5 and process a document with a \verb+tabular+ +environment.) (See the definitions of \verb+\strutbox+ and of \verb+\@array+ +in \verb+latex.ltx+.) + +\verb+sgame.sty+ makes the vertical distance between the lines at the top and +bottom of a row of a \verb+game+ the same (\verb+\arraystretch+ times +\verb+\baselineskip+), but places the baseline of the text in each cell so +that the distances above and below an upper case I placed on the baseline are +equal. (See the right panel of Figure~\ref{f:VertPos}.) (If you'd like to +use another character, define this character to be \verb+\sg@alignchar+.) +\begin{figure}[htb] +\hspace*{\fill} +\begin{pspicture}(80,55) +\psline(0,5)(30,5) +\psline(0,55)(30,55) +\psline[linecolor=lightgray](0,20)(30,20) +\rput[B](15,20){\fontsize{14mm}{10mm}\selectfont AygIx} +\psline[linecolor=lightgray]{<->}(15,5)(15,20) +\rput*(15,12.5){$0.3d$} +\psline[linecolor=lightgray]{<->}(15,20)(15,55) +\rput*(15,37.5){$0.7d$} +\rput[B](15,0){\texttt{tabular} environment} +% +\psline[linecolor=lightgray]{<->}(40,5)(40,55) +\rput*(40,30){$d$} +% +\psline(50,5)(80,5) +\psline(50,55)(80,55) +\psline[linecolor=lightgray](50,25)(80,25) +\psline[linecolor=lightgray](50,35)(80,35) +\rput[B](65,25){\fontsize{14mm}{10mm}\selectfont AygIx} +\psline[linecolor=lightgray]{<->}(65,5)(65,25) +\rput*(65,15){$x$} +\psline[linecolor=lightgray]{<->}(65,35)(65,55) +\rput*(65,45){$x$} +\rput[B](65,0){\texttt{game} environment} +\end{pspicture} +\hspace*{\fill} +\caption[]{Vertical positioning of text within cells in the \texttt{tabular} +and \texttt{game} environments.}\label{f:VertPos} +\end{figure} + +If you want to use \verb+sgame+'s vertical positioning in your \verb+tabular+ +environments, as well as your \verb+game+ environments, set +\verb+\gamevaligntrue+ before the environment. (If you want to switch back at +some point, you can do so by setting \verb+\gamevalignfalse+.) + +If the height of the text in a cell exceeds \verb+\arraystretch+ times +\verb+\baselineskip+, then the height of the row is increased to accommodate +the text (just as the distance between lines of text is increased to +accommodate large text). The result is that the lines at the top and bottom +of the row touch the top and bottom of the text, and this row is taller than +the others. To improve the appearance of the table you may want to increase +\verb+\gamestretch+ (analogous to \verb+\arraystretch+), to put some white +space above and below your oversized text. + +When \verb+\gamestretch+ is increased from 1, the height of \emph{every} row, +including the first row (the action labels), is increased. If you don't want +to increase the space under the action labels, declare \verb+\ssualfalse+. +(``ssual'' stands for ``stretch space under action labels''.) See +Figures~\ref{f:ssual1} and \ref{f:ssual2} for examples (for games with and +without player labels).% +\begin{figure}[htb]\hspace*{\fill}\renewcommand{\gamestretch}{3}% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$2,1$&$2,2$\\ +$B$&$3,3$&$4,4$ +\end{game}% +\hspace*{\fill}% +\ssualfalse% +\begin{game}{2}{2} +&$L$&$R$\\ +$T$&$2,1$&$2,2$\\ +$B$&$3,3$&$4,4$ +\end{game}% +\hspace*{\fill}% +\caption[]{Positioning the action labels of the column player when +\texttt{gamestretch} is larger than 1, for a game without player labels. In +the left game we have \texttt{ssualtrue} (the default); in the right game +\texttt{ssualfalse} is declared.}\label{f:ssual2} +\end{figure} +\begin{figure}[htb]\hspace*{\fill}\renewcommand{\gamestretch}{3}% +\begin{game}{2}{2}[Player 1][Player 2] +&$L$&$R$\\ +$T$&$2,1$&$2,2$\\ +$B$&$3,3$&$4,4$ +\end{game}% +\hspace*{\fill}% +\ssualfalse% +\begin{game}{2}{2}[Player 1][Player 2] +&$L$&$R$\\ +$T$&$2,1$&$2,2$\\ +$B$&$3,3$&$4,4$ +\end{game}% +\hspace*{\fill}% +\caption[]{Positioning the action labels of the column player when +\texttt{gamestretch} is larger than 1, for a game with player labels. In the +left game we have \texttt{ssualtrue} (the default); in the right game +\texttt{ssualfalse} is declared.}\label{f:ssual1} +\end{figure} +\section{Parameters}\label{s:param} +\verb+\gamestretch+: a number that controls the spacing between rows, +analogous to \verb+\arraystretch+. Possible values: positive real numbers. +Default: value of \verb+\arraystretch+ when \verb+sgame.sty+ is loaded (1 in +standard styles). Example: \verb+\renewcommand{\gamestretch}{2}+. + +\vspace{4mm} + +\noindent\verb+\sgcolsep+: horizontal padding within cells. Possible values: +any dimension. Default: value of \verb+\tabcolsep+ when \verb+sgame.sty+ is +loaded. Example: \verb+\sgcolsep=10pt+. + +\vspace{4mm} + +\noindent\verb+\sglabelsep+: vertical space between game and label. Possible +values: any dimension. Default: 5pt. Example: \verb+\sglabelsep=10pt+. + +\vspace{4mm} + +\noindent\verb+\irpawcgltrue+ (``include row player actions when centering +game label''): causes game label to be centered under box consisting of row +player actions and payoff matrix. Default: \verb+\irpawcglfalse+ (i.e.\ game +label is centered under box consisting only of payoff matrix). Example: +\verb+\irpawcgltrue+. + +\vspace{4mm} + +\noindent\verb+\irplwcgltrue+ (``include row player label when centering game +label''): causes game label to be centered under box consisting of row player +label, row player actions, and payoff matrix. (Is overridden by +\verb+\irpawcgltrue+.) Default: \verb+\irplwcglfalse+ (i.e.\ game label is +centered under payoff matrix). Example: \verb+\irplwcgltrue+. + +\vspace{4mm} + +\noindent\verb+\gamemathtrue+: put all text in cells in payoff matrix in math +mode. Default: \verb+\gamemathfalse+. Example: \verb+\gamemathtrue+. + +\vspace{4mm} + +\noindent\verb+\gamevaligntrue+: vertically align the text within cells of a +\verb+tabular+ environment as they are aligned in a \verb+game+ environment. +Default: \verb+\gamevalignfalse+. Example: \verb+\gamevaligntrue+. (See +Section~\ref{s:VertPos}.) + +\vspace{4mm} + +\noindent\verb+\ssualtrue+: stretch space under action labels when +\verb+\gamestretch+ is greater than 1. Default: \verb+\ssualtrue+. Example: +\verb+\ssualfalse+. (See Section~\ref{s:VertPos}.) + +\vspace{4mm} + +\noindent\verb+\sglinecolor+: color of lines around payoffs. Default: +\verb+black+. Example: \verb+\def\sglinecolor{lightgray}+. + +\vspace{4mm} + +\noindent\verb+\sgtextcolor+: color of text in game (action labels, payoffs, +player labels). Default: \verb+black+. Example: +\verb+\def\sgtextcolor{blue}+. +\section{History} +\subsection*{Version 1} +\begin{description} +\item[1993/12] First version. +\end{description} +\subsection*{Version 2} +\begin{description} +\item[1997/10] Labels allowed (via additional optional argument). Parameters +added: \verb+\sglabelsep+, \verb+\sgcolsep+, \verb+\irplwcgltrue+, +\verb+\irpawcgltrue+, and \verb+\gamemathtrue+. +\item[2002/6 (version 2.1)] Modification of \LaTeX's \verb+\@array+ changed so +that it does not change spacing in \verb+tabular+ environment. Color +functionality added. Parameters added: \verb+\gamevaligntrue+, +\verb+\ssualtrue+ (allowing more control over vertical spacing when +\verb+\gamestretch+ is greater than 1), \verb+\sglinecolor+, +\verb+\sgtextcolor+. +\item[2004/5/13 (version 2.11)] Minor bug fix. +\item[2004/5/21 (version 2.12)] Minor bug fix. +\item[2005/7/8 (version 2.13)] Minor bug fix. +\end{description} + +} + +\end{document} + |