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\begin{document}

\title{\textsf{Graphics Code for} \\
\textsf{The Politics of the First World War:} \\ \textsf{A Course in Game Theory and International Security}}
\author{Scott Wolford \\ University of Texas \\ \href{mailto:swolford@austin.utexas.edu}{swolford@austin.utexas.edu}}
\date{Updated \today }
\maketitle

\frontmatter 

\tableofcontents

\listoffigures

\chapter{Timeline of Key Events}

\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
	\draw[thick](0,0)--(0,-9.4);
\node [left] at (-0.1,0) {1905};
	\draw[thick](-0.1,0)--(0.1,0);
	\draw[thick,dotted](0.2,0)--(5.5,0);
	\draw[thick](5.5,0.25)--(5.5,-0.25);
	\node [right] at (5.5,0.2) {Russo-Japanese War Ends (Ch. \ref{ch:war4})};
	\node [right] at (5.5,-0.2) {First Moroccan Crisis (Ch. \ref{ch:outbreak})};
\node [left] at (-0.1,-0.4) {1906};
	\draw[thick](-0.1,-0.4)--(0.1,-0.4);
	\node [right] at (0.1,-0.4) {Anglo-German naval race begins (Ch. \ref{ch:navalrace})};
\node[left] at (-0.1,-0.8) {1911};
	\draw[thick](-0.1,-0.8)--(0.1,-0.8);
	\node [right] at (0.1,-0.8) {Second Moroccan Crisis (Ch. \ref{ch:outbreak})};
\node[left] at (-0.1,-1.2) {1912};
	\draw[thick](-0.1,-1.2)--(0.1,-1.2);
	\draw[thick, dotted](0.2,-1.2)--(4.5,-1.2);
	\draw[thick](4.5,-0.95)--(4.5,-1.45);
	\node [right] at (4.5,-1) {Anglo-German naval race ends (Ch. \ref{ch:navalrace})};
	\node [right] at (4.5,-1.4) {First Balkan War begins (Ch. \ref{ch:outbreak})};
\node[left] at (-0.1,-2.2) {1913};
	\draw[thick] (-0.1,-2.2)--(0.1,-2.2);
	\draw[thick] (0.1,-1.55)--(0.1,-2.85);
	\node[right] at (0.1,-1.6) {First Balkan War ends (Ch. \ref{ch:outbreak})};
	\node[right] at (0.1,-2) {Second Balkan War (Ch. \ref{ch:outbreak})};
	\node[right] at (0.1,-2.4) {Liman von Sanders crisis (Ch. \ref{ch:outbreak})}; 
	\node[right] at (0.1,-2.8) {General army expansions (Ch. \ref{ch:outbreak})}; 
\node[left] at (-0.1,-3.8) {1914};
	\draw[thick] (-0.1,-3.8)--(0.1,-3.8);
	\draw[thick,dotted] (0.2,-3.8)--(4.75,-3.8);
	\draw[thick] (4.75,-2.15)--(4.75,-5.45);
	\node[right] at (4.75,-2.2) {Sarajevo assassinations (Ch. \ref{ch:outbreak})};
	\node[right] at (4.75,-2.6) {July Crisis (Ch. \ref{ch:outbreak})};
	\node[right] at (4.75,-3) {British entry (Ch. \ref{ch:belgium})};
	\node[right] at (4.75,-3.4) {Battle of the Frontiers (Ch. \ref{ch:coalitions})};
	\node[right] at (4.75,-3.8) {Battle of Heligoland Bight (Ch. \ref{ch:haul})};
	\node[right] at (4.75,-4.2) {First Battle of the Marne (Ch. \ref{ch:attrition})};
	\node[right] at (4.75,-4.6) {Ottomans join Central Powers (Ch. \ref{ch:choosing})};
	\node[right] at (4.75,-5) {Japan declares war on Germany (Ch. \ref{ch:choosing})};
	\node[right] at (4.75,-5.4) {First Battle of Ypres (Ch. \ref{ch:attrition})};
\node[left] at (-0.1,-5.6) {1915};
	\draw[thick] (-0.1,-5.6)--(0.1,-5.6);
	\draw[thick] (0.1,-4.75)--(0.1,-6.45);
	\node[right] at (0.1,-4.8) {Battle of Dogger Bank (Ch. \ref{ch:haul})};
	\node[right] at (0.1,-5.2) {Gorlice-Tarn\'ow offensive (Ch. \ref{ch:attrition})};
	\node[right] at (0.1,-5.6) {Italy joins Entente (Ch. \ref{ch:choosing})};
	\node[right] at (0.1,-6) {German \emph{Sussex} Pledge (Ch. \ref{ch:merica})};
	\node[right] at (0.1,-6.4) {Japan issues ``21 Demands'' (Ch. \ref{ch:choosing})};
\node[left] at (-0.1,-6.8) {1916};
	\draw[thick] (-0.1,-6.8)--(0.1,-6.8);
	\draw[thick,dotted] (0.2,-6.8)--(5.5,-6.8);
	\draw[thick] (5.5,-6.15)--(5.5,-7.45);
	\node[right] at (5.5,-6.2) {Battle of Verdun (Ch. \ref{ch:attrition})};
	\node[right] at (5.5,-6.6) {Battle of Jutland-Skaggerak (Ch. \ref{ch:haul})};
	\node[right] at (5.5,-7) {Battle of the Somme (Ch. \ref{ch:attrition})};
	\node[right] at (5.5,-7.4) {Brusilov Offensive (Ch. \ref{ch:attrition})};
\node[left] at (-0.1,-7.8) {1917};
	\draw[thick](-0.1,-7.8)--(0.1,-7.8);
	\draw[thick](0.1,-7.2)--(0.1,-8.4);
	\node[right] at (0.1,-7.2) {``Peace Without Victory'' speech (Ch. \ref{ch:merica})};
	\node[right] at (0.1,-7.6) {Germany unleashes U-boats (Ch. \ref{ch:merica})};
	\node[right] at (0.1,-8) {U.S. declares war on Germany (Ch. \ref{ch:merica})};
	\node[right] at (0.1,-8.4) {China declares war on Germany (Ch. \ref{ch:choosing})};
\node[left] at (-0.1,-8.8) {1918};
	\draw[thick](-0.1,-8.8)--(0.1,-8.8);
	\draw[thick] (5.5,-8.15)--(5.5,-9.45);
	\draw[thick,dotted](0.2,-8.8)--(5.5,-8.8);
	\node[right] at (5.5,-8.2) {Treaty of Brest-Litovsk (Ch. \ref{ch:merica})};
	\node[right] at (5.5,-8.6) {German Spring Offensive (Ch. \ref{ch:termination})};
	\node[right] at (5.5,-9) {Bulgaria requests armistice (Ch. \ref{ch:termination})};
	\node[right] at (5.5,-9.4) {Germany requests armistice (Ch. \ref{ch:termination})};
\node[left] at (-0.1,-9.4) {1919};
	\draw[thick](-0.1,-9.4)--(0.1,-9.4);
	\draw[thick](0.1,-9.15)--(0.1,-9.65);
	\node[right] at (0.1,-9.2) {Treaty of Versailles (Ch. \ref{ch:termination})};
	\node[right] at (0.1,-9.6) {U.S. fails to ratify Versailles (Ch. \ref{ch:termination})};
\end{tikzpicture}
\end{center}

\mainmatter

\chapter{Introduction: \\ The Great War}
\chaptermark{The Great War}
\label{ch:introduction}
\bigskip

No graphics.

\chapter{The Theory of War I: \\ Commitment Problems}
\chaptermark{The Theory of War I}
\label{ch:models}
\bigskip

\begin{figure}
\caption{Players, Actions, and Outcomes}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {war}; % bottom left
\node at (0.8,0.9) {split}; % upper left
\node at (2.4,0.3) {A wins}; % bottom right
\node at (2.4,0.9) {split}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {B};
% social optimum
%\draw[thick,blue](0.25,0.6)--(0.25,0.9);
%\draw[thick,blue](0.25,0.6)--(0.75,0.6);
%\draw[thick,blue](0.75,0.6)--(0.75,0.9);
%\draw[thick,blue](0.75,0.9)--(0.25,0.9);
% Nash equilibrium
%\draw[thick,red](1.25,0.1)--(1.75,0.1);
%\draw[thick,red](1.75,0.1)--(1.75,0.4);
%\draw[thick,red](1.75,0.4)--(1.25,0.4);
%\draw[thick,red](1.25,0.4)--(1.25,0.1);
\end{tikzpicture}
\end{center}
\label{fig:models_PACs}
\end{figure}

\begin{figure}
\caption{Players, Actions, Outcomes, and Payoffs}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 3}; % bottom left
\node at (0.8,0.9) {2, 4}; % upper left
\node at (2.4,0.3) {4, 1}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {B};
% social optimum
%\draw[thick,blue](0.25,0.6)--(0.25,0.9);
%\draw[thick,blue](0.25,0.6)--(0.75,0.6);
%\draw[thick,blue](0.75,0.6)--(0.75,0.9);
%\draw[thick,blue](0.75,0.9)--(0.25,0.9);
% Nash equilibrium
%\draw[thick,red](1.25,0.1)--(1.75,0.1);
%\draw[thick,red](1.75,0.1)--(1.75,0.4);
%\draw[thick,red](1.75,0.4)--(1.25,0.4);
%\draw[thick,red](1.25,0.4)--(1.25,0.1);
\end{tikzpicture}
\end{center}
\label{fig:models_PACPs}
\end{figure}

\begin{figure}
\caption{An Example of a Nash Equilibrium}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 3}; % bottom left
\node at (0.8,0.9) {2, 4}; % upper left
\node at (2.4,0.3) {4, 1}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {B};
% Nash equilibrium
\draw[thick,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:models_eqm1}
\end{figure}

\begin{figure}
\caption{The Inefficiency of War}
\begin{center}
\begin{tikzpicture}[scale=1.5]
    \node [below] at (-1,2) {\small{If C and D negotiate.}};
\draw[thick] (-1,0) circle [radius=1.5];
\draw[thick, dashed, gray] (-1,1.5)--(-1,-1.5);
    \node at (-1.75,0) {\small{C}};
    \node at (-0.25,0) {\small{D}};
    \node [below] at (3,2) {\small{If C and D fight.}};
\draw[thick] (3,0) circle [radius=1];
\draw[thick, dashed, gray] (3,1)--(3,-1);
    \node at (2.5,0) {\small{C}};
    \node at (3.5,0) {\small{D}};
\end{tikzpicture}
\end{center}
\label{fig:models_inefficiency}
\end{figure}

\begin{figure}
\caption{Commitment Problems and War}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {2, 2}; % bottom left
\node at (0.8,0.9) {4, 3}; % upper left
\node at (2.4,0.3) {3, 2}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {pass};
\node [left] at (-0.2,0.3) {attack};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {honor};
\node [above] at (2.4,1.4) {renege};
\node [above] at (1.6,1.9) {B};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Social optimum
\draw[thick,dashed](0.3,0.7)--(1.3,0.7);
\draw[thick,dashed](0.3,1.1)--(1.3,1.1);
\draw[thick,dashed](0.3,0.7)--(0.3,1.1);
\draw[thick,dashed](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:models_preventive}
\end{figure}

\chapter{Armed Continent: \\ The Anglo-German Naval Race}
\chaptermark{Armed Continent}
\label{ch:navalrace}
\bigskip

\begin{figure}
\caption{From \emph{Dreadnought} to Naval Race, 1905-1912}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (0,-0.1) {1905};
	\draw[thick](0,0.1)--(0,-0.1);
	\node[above] at (0,0.1) {HMS \emph{Dreadnought}};
\node[below] at (2,-0.1) {1906};
	\draw[thick](2,0.1)--(2,-0.1);
	\draw[thick,dotted](2,0.1)--(2,0.75);
	\node[above] at (2,0.75) {Major German naval bill};
\node[below] at (4,-0.1) {1910};
	\draw[thick](4,0.1)--(4,-0.1);
	\node[above] at (4,0.1) {Major British naval bill};
\node[below] at (6,-0.1) {1912};
	\draw[thick](6,0.1)--(6,-0.1);
	\draw[thick,dotted](6,0.1)--(6,0.75);
	\node[above] at (6,0.75) {Germany abandons race};
\end{tikzpicture}
\end{center}
\label{fig:navalrace_timeline}
\end{figure}


\begin{figure}
\caption{The Anglo-German naval race}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {4, 1}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {2, 2}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {$\neg$build};
\node [left] at (-0.2,0.3) {build};
\node [left] at (-1.2,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {$\neg$build};
\node [above] at (2.4,1.4) {build};
\node [above] at (1.6,1.9) {Germany};
% social optimum
%\draw[thick,blue](0.25,0.6)--(0.25,0.9);
%\draw[thick,blue](0.25,0.6)--(0.75,0.6);
%\draw[thick,blue](0.75,0.6)--(0.75,0.9);
%\draw[thick,blue](0.75,0.9)--(0.25,0.9);
% Nash equilibrium
%\draw[thick,red](1.25,0.1)--(1.75,0.1);
%\draw[thick,red](1.75,0.1)--(1.75,0.4);
%\draw[thick,red](1.75,0.4)--(1.25,0.4);
%\draw[thick,red](1.25,0.4)--(1.25,0.1);
\end{tikzpicture}
\end{center}
\label{fig:navalrace_navalgame}
\end{figure}

\begin{figure}
\caption{The Anglo-German naval race}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {4, 1}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {2, 2}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {$\neg$build};
\node [left] at (-0.2,0.3) {build};
\node [left] at (-1.2,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {$\neg$build};
\node [above] at (2.4,1.4) {build};
\node [above] at (1.6,1.9) {Germany};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Social optimum
\draw[thick,dashed](0.3,0.7)--(1.3,0.7);
\draw[thick,dashed](0.3,1.1)--(1.3,1.1);
\draw[thick,dashed](0.3,0.7)--(0.3,1.1);
\draw[thick,dashed](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:navalrace_navalgame_eq}
\end{figure}

\chapter{Leaping Into the Dark: \\ Europe Goes to War}
\chaptermark{Leaping Into the Dark}
\label{ch:outbreak}
\bigskip

\begin{figure}
\caption{The Path to War, 1905-1914}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (-1,-0.1) {1905};
	\draw[thick](-1,0.1)--(-1,-0.1);
	\node[above] at (-1,0.1) {1st Moroccan Crisis};
\node[below] at (1,-0.1) {1911};
	\draw[thick](1,0.1)--(1,-0.1);
	\draw[thick,dotted](1,0.1)--(1,0.75);
	\node[above] at (1,0.75) {2nd Moroccan Crisis};
\node[below] at (3,-0.1) {1912};
	\draw[thick](3,0.1)--(3,-0.1);
	\node[above] at (3,0.1) {1st Balkan War};
\node[below] at (5,-0.1) {1913};
	\draw[thick](5,-0.1)--(5,0.1);
	\draw[thick,dotted](5,0.1)--(5,0.75);
	\node[above] at (5,0.75) {Liman von Sanders Crisis};
	\node[above] at (5,1.05) {2nd Balkan War};
\node[below] at (7,-0.1) {1914};
	\draw[thick](7,-0.1)--(7,0.1);
	\node[above] at (7,0.1) {July Crisis};
\end{tikzpicture}
\end{center}
\label{fig:outbreak_timeline}
\end{figure}

\begin{figure}
\caption{The Austro-Serb Crisis}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {2, 2}; % bottom left
\node at (0.8,0.9) {4, 1}; % upper left
\node at (2.4,0.3) {3, 3}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {pass};
\node [left] at (-0.2,0.3) {attack};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {honor};
\node [above] at (2.4,1.4) {refuse};
\node [above] at (1.6,1.9) {S};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Social optimum
%\draw[thick,blue](0.3,0.7)--(1.3,0.7);
%\draw[thick,blue](0.3,1.1)--(1.3,1.1);
%\draw[thick,blue](0.3,0.7)--(0.3,1.1);
%\draw[thick,blue](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:outbreak_austro-serb}
\end{figure}

\begin{figure}
\caption{Russia and the July Crisis}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {2, 2}; % bottom left
\node at (0.8,0.9) {4, 1}; % upper left
\node at (2.4,0.3) {3, 3}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {pass};
\node [left] at (-0.2,0.3) {attack};
\node [left] at (-1.2,0.6) {R};
% column player
\node [above] at (0.8,1.4) {pass};
\node [above] at (2.4,1.4) {attack S};
\node [above] at (1.6,1.9) {A};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Social optimum
%\draw[thick,blue](0.3,0.7)--(1.3,0.7);
%\draw[thick,blue](0.3,1.1)--(1.3,1.1);
%\draw[thick,blue](0.3,0.7)--(0.3,1.1);
%\draw[thick,blue](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:outbreak_russo-austrian}
\end{figure}

\begin{figure}
\caption{Germany and Russia in the July Crisis}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {4, 1}; % bottom left
\node at (0.8,0.9) {3, 1}; % upper left
\node at (2.4,0.3) {2, 3}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {abandon};
\node [left] at (-0.2,0.3) {support};
\node [left] at (-1.5,0.6) {G};
% column player
\node [above] at (0.8,1.4) {abandon};
\node [above] at (2.4,1.4) {support};
\node [above] at (1.6,1.9) {R};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Social optimum
%\draw[thick,blue](0.3,0.7)--(1.3,0.7);
%\draw[thick,blue](0.3,1.1)--(1.3,1.1);
%\draw[thick,blue](0.3,0.7)--(0.3,1.1);
%\draw[thick,blue](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:outbreak_russo-german}
\end{figure}

\chapter{The Theory of War II: \\ Information Problems}
\chaptermark{The Theory of War II}
\label{ch:tools2}
\bigskip

\begin{figure}
\caption{A Game With Unknown Preferences}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {3, ?}; % bottom left
\node at (0.8,0.9) {2, 4}; % upper left
\node at (2.4,0.3) {4, ?}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {B};
% social optimum
%\draw[thick,blue](0.25,0.6)--(0.25,0.9);
%\draw[thick,blue](0.25,0.6)--(0.75,0.6);
%\draw[thick,blue](0.75,0.6)--(0.75,0.9);
%\draw[thick,blue](0.75,0.9)--(0.25,0.9);
% Nash equilibrium
%\draw[thick,red](0.3,0.1)--(1.3,0.1);
%\draw[thick,red](0.3,0.1)--(0.3,0.5);
%\draw[thick,red](0.3,0.5)--(1.3,0.5);
%\draw[thick,red](1.3,0.1)--(1.3,0.5);
\end{tikzpicture}
\end{center}
\label{fig:tools2_bayesex}
\end{figure}

\begin{figure}
\caption{Uncertainty and Subjective Probabilities}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% number line
\draw[thick](0,0)--(8,0);
\draw[thick](0,-0.1)--(0,0.5);
\draw[thick](2,0.1)--(2,-0.1);
%\draw[thick](4,0.1)--(4,-0.1);
\draw[thick](4,-0.1)--(4,0.5);
\draw[thick](6,0.1)--(6,-0.1);
\draw[thick](8,-0.1)--(8,0.5);
% ticks
\node [below] at (0,-0.1) {0};
\node [above] at (0,0.5) {irresolute};
\node [below] at (2,-0.1) {0.25};
\node [below] at (4,-0.1) {0.5};
\node [above] at (4,0.5) {maximal uncertainty};
\node [below] at (6,-0.1) {0.75};
\node [below] at (8,-0.1) {1};
\node [above] at (8,0.5) {resolute};
% title
\node at (4,-1) {1's Subjective Probability that 2 is Resolute ($r$)};
\end{tikzpicture}
\end{center}
\label{fig:tools2_beliefs}
\end{figure}

\begin{figure}
\caption{An Example of a Bayesian Game}
\begin{center}
%insatiable
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 3}; % bottom left
\node at (0.8,0.9) {2, 4}; % upper left
\node at (2.4,0.3) {4, 1}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.1,0.6) {1};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {2 (resolute)};
\node at (1.6,-0.5) {$\Pr(\text{resolute})=r$};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
% satiable
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {3, 1}; % bottom left
\node at (0.8,0.9) {2, 4}; % upper left
\node at (2.4,0.3) {4, 3}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.1,0.6) {1};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {2 (irresolute)};
\node at (1.6,-0.5) {$\Pr(\text{irresolute})=1-r$};
% Nash equilibrium
%\draw[dashed,red](1.9,0.1)--(2.9,0.1);
%\draw[dashed,red](1.9,0.1)--(1.9,0.5);
%\draw[dashed,red](1.9,0.5)--(2.9,0.5);
%\draw[dashed,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:tools2_bayesiangames1}
\end{figure}

\begin{figure}
\caption{Information Problems and War}
\begin{center}
%insatiable
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 3}; % bottom left
\node at (0.8,0.9) {2, 4}; % upper left
\node at (2.4,0.3) {4, 1}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.1,0.6) {1};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {2 (resolute)};
\node at (1.6,-0.5) {$\Pr(\text{resolute})=r$};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
\draw[dashed,gray](0.3,0.7)--(1.3,0.7);
\draw[dashed,gray](0.3,1.1)--(1.3,1.1);
\draw[dashed,gray](0.3,0.7)--(0.3,1.1);
\draw[dashed,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
% satiable
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {3, 1}; % bottom left
\node at (0.8,0.9) {2, 4}; % upper left
\node at (2.4,0.3) {4, 3}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {half};
\node [left] at (-0.2,0.3) {all};
\node [left] at (-1.1,0.6) {1};
% column player
\node [above] at (0.8,1.4) {half};
\node [above] at (2.4,1.4) {all};
\node [above] at (1.6,1.9) {2 (irresolute)};
\node at (1.6,-0.5) {$\Pr(\text{irresolute})=1-r$};
% Nash equilibrium
\draw[dashed,gray](1.9,0.1)--(2.9,0.1);
\draw[dashed,gray](1.9,0.1)--(1.9,0.5);
\draw[dashed,gray](1.9,0.5)--(2.9,0.5);
\draw[dashed,gray](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.1)--(1.3,0.1);
%\draw[dashed,red](0.3,0.5)--(1.3,0.5);
%\draw[dashed,red](0.3,0.1)--(0.3,0.5);
%\draw[dashed,red](1.3,0.1)--(1.3,0.5);
\end{tikzpicture}
\end{center}
\label{fig:tools2_bayesiangames2}
\end{figure}

\begin{figure}
\caption{Unique and Overlapping Equilibria}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% number line
\draw[thick](0,0)--(8,0);
\draw[thick](0,-0.1)--(0,0.1);
\draw[thick](4,-0.1)--(4,0.1);
\draw[thick](5.3,0.1)--(5.3,-0.1);
\draw[thick](8,-0.1)--(8,0.1);
% ticks
\node [below] at (0,-0.1) {0};
\node [below] at (4,-0.1) {1/2};
\node [below] at (5.3,-0.1) {2/3};
\node [below] at (8,-0.1) {1};
% title
\node at (4,-1) {A's Belief that B is Resolute ($r$)};
% equilibria
\draw[thick, decoration={brace},decorate](0,0.5)--(5.3,0.5);
		\node [above] at (2.65,0.55) {(all: $r\leq2/3$; half, all)};
		\draw[thick, dotted](0,0.1)--(0,0.5);
		\draw[thick, dotted](5.3,0.1)--(5.3,0.5);
\draw[thick, decoration={brace},decorate](4,1)--(8,1);
		\node [above] at (6,1.05) {(half: $r>1/2$; half, half)};
		\draw[thick, dotted](4,0.1)--(4,1);
		\draw[thick, dotted](8,0.1)--(8,1);
\end{tikzpicture}
\end{center}
\label{fig:tools2_uniqueness}
\end{figure}

\begin{figure}
\caption{The Principal-Agent Problem in Military Strategy}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 1}; % bottom left
\node at (0.8,0.9) {4, 3}; % upper left
\node at (2.4,0.3) {1, 1}; % bottom right
\node at (2.4,0.9) {5, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {either};
\node [left] at (-0.2,0.3) {neither};
%\node [left] at (-0.2,-0.3) {never};
\node [left] at (-1.1,0.6) {P};
% column player
\node [above] at (0.8,1.4) {wait};
\node [above] at (2.4,1.4) {now};
\node [above] at (1.6,1.9) {G (defensive)};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {3, 1}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {3, 1}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {either};
\node [left] at (-0.2,0.3) {neither};
\node [left] at (-1.1,0.6) {P};
% column player
\node [above] at (0.8,1.4) {wait};
\node [above] at (2.4,1.4) {now};
\node [above] at (1.6,1.9) {G (expansionist)};
% Nash equilibrium
%\draw[dashed,red](1.9,0.1)--(2.9,0.1);
%\draw[dashed,red](1.9,0.1)--(1.9,0.5);
%\draw[dashed,red](1.9,0.5)--(2.9,0.5);
%\draw[dashed,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:domestic_pa1}
\end{figure}

\begin{figure}
\caption{Solving the Principal-Agent Problem in Military Strategy}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,-0.6)--(0,1.2);
\draw[thick](3.2,-0.6)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,-0.6)--(1.6,1.2);
\draw[thick](0,-0.6)--(3.2,-0.6);
% payoffs
\node at (0.8,0.3) {4, 3}; % bottom left
\node at (0.8,0.9) {4, 3}; % upper left
\node at (2.4,0.3) {1, 1}; % bottom right
\node at (2.4,0.9) {5, 4}; % upper right
\node at (0.8,-0.3) {1, 1};
\node at (2.4,-0.3) {1, 1};
% row player
\node [left] at (-0.2,0.9) {either};
\node [left] at (-0.2,0.3) {wait};
\node [left] at (-0.2,-0.3) {neither};
\node [left] at (-1.1,0.3) {P};
% column player
\node [above] at (0.8,1.4) {wait};
\node [above] at (2.4,1.4) {now};
\node [above] at (1.6,1.9) {G (defensive)};
% Nash equilibrium
\draw[thick,gray](0.3,0.1)--(1.3,0.1);
\draw[thick,gray](0.3,0.1)--(0.3,0.5);
\draw[thick,gray](0.3,0.5)--(1.3,0.5);
\draw[thick,gray](1.3,0.1)--(1.3,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,-0.6)--(0,1.2);
\draw[thick](3.2,-0.6)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,-0.6)--(1.6,1.2);
\draw[thick](0,-0.6)--(3.2,-0.6);
% payoffs
\node at (0.8,0.3) {3, 3}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {3, 1}; % bottom right
\node at (2.4,0.9) {2, 4}; % upper right
\node at (0.8,-0.3) {3, 1};
\node at (2.4,-0.3) {3, 1};
% row player
\node [left] at (-0.2,0.9) {either};
\node [left] at (-0.2,0.3) {wait};
\node [left] at (-0.2,-0.3) {neither};
\node [left] at (-1.1,0.3) {P};
% column player
\node [above] at (0.8,1.4) {wait};
\node [above] at (2.4,1.4) {now};
\node [above] at (1.6,1.9) {G (expansionist)};
% Nash equilibrium
\draw[thick,gray](0.3,0.1)--(1.3,0.1);
\draw[thick,gray](0.3,0.1)--(0.3,0.5);
\draw[thick,gray](0.3,0.5)--(1.3,0.5);
\draw[thick,gray](1.3,0.1)--(1.3,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:domestic_pa2}
\end{figure}

\chapter{A Scrap of Paper: \\ Belgium, France, and British Entry}
\chaptermark{A Scrap of Paper}
\label{ch:belgium}
\bigskip

\begin{figure}
\caption{The Violation and Defense of Belgium, August 1914}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (0,-0.1) {1 August};
	\draw[thick](0,0.1)--(0,-0.1);
	\node[above] at (0,0.1) {Germany \& France mobilize};
\node[below] at (2,-0.1) {2 August};
	\draw[thick](2,0.1)--(2,-0.1);
	\draw[thick,dotted](2,0.1)--(2,0.75);
	\node[above] at (2,0.75) {German ultimatum to Belgium};
\node[below] at (4,-0.1) {3 August};
	\draw[thick](4,0.1)--(4,-0.1);
	\node[above] at (4,0.1) {Ger. declares war on France};
\node[below] at (6,-0.1) {4 August};
	\draw[thick](6,0.1)--(6,-0.1);
	\draw[thick,dotted](6,0.1)--(6,0.75);
	\node[above] at (6,0.75) {UK declares war on Ger.};
	\node[above] at (6,1.05) {Germany invades Belgium};
\end{tikzpicture}
\end{center}
\label{fig:belgium_timeline}
\end{figure}

\begin{figure}
\caption{German Goals and Britain's Strategic Problem}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 4}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {1, 2}; % bottom right
\node at (2.4,0.9) {3, 1}; % upper right
% row player
\node [left] at (-0.2,0.9) {fight};
\node [left] at (-0.2,0.3) {$\neg$fight};
\node [left] at (-1.1,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {offense};
\node [above] at (2.4,1.4) {defense};
\node [above] at (1.6,1.9) {G (unlimited)};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
\draw[dashed,gray](0.3,0.7)--(1.3,0.7);
\draw[dashed,gray](0.3,1.1)--(1.3,1.1);
\draw[dashed,gray](0.3,0.7)--(0.3,1.1);
\draw[dashed,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 2}; % bottom left
\node at (0.8,0.9) {2, 1}; % upper left
\node at (2.4,0.3) {4, 4}; % bottom right
\node at (2.4,0.9) {1, 3}; % upper right
% row player
\node [left] at (-0.2,0.9) {fight};
\node [left] at (-0.2,0.3) {$\neg$fight};
\node [left] at (-1.1,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {offense};
\node [above] at (2.4,1.4) {defense};
\node [above] at (1.6,1.9) {G (limited)};
% Nash equilibrium
\draw[dashed,gray](1.9,0.1)--(2.9,0.1);
\draw[dashed,gray](1.9,0.1)--(1.9,0.5);
\draw[dashed,gray](1.9,0.5)--(2.9,0.5);
\draw[dashed,gray](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:belgium_germany-britain1}
\end{figure}

\begin{figure}
\caption{German Strategy and Belgian Neutrality}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 4}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {4, 1}; % bottom right
\node at (2.4,0.9) {4, 1}; % upper right
% row player
\node [left] at (-0.2,0.9) {resist};
\node [left] at (-0.2,0.3) {acq};
\node [left] at (-1.1,0.6) {B};
% column player
\node [above] at (0.8,1.4) {violate};
\node [above] at (2.4,1.4) {honor};
\node [above] at (1.6,1.9) {G (unlimited)};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
\draw[thick,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 2}; % bottom left
\node at (0.8,0.9) {3, 1}; % upper left
\node at (2.4,0.3) {4, 3}; % bottom right
\node at (2.4,0.9) {4, 3}; % upper right
% row player
\node [left] at (-0.2,0.9) {resist};
\node [left] at (-0.2,0.3) {acq};
\node [left] at (-1.1,0.6) {B};
% column player
\node [above] at (0.8,1.4) {violate};
\node [above] at (2.4,1.4) {honor};
\node [above] at (1.6,1.9) {G (limited)};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
\draw[thick,gray](1.9,0.7)--(2.9,0.7);
\draw[thick,gray](1.9,1.1)--(2.9,1.1);
\draw[thick,gray](1.9,0.7)--(1.9,1.1);
\draw[thick,gray](2.9,0.7)--(2.9,1.1);
\end{tikzpicture}
\end{center}
\label{fig:belgium_germany-belgium}
\end{figure}

\begin{figure}
\caption{Germany's Aims and British Intervention}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 4}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {1, 2}; % bottom right
\node at (2.4,0.9) {3, 1}; % upper right
% row player
\node [left] at (-0.2,0.9) {fight};
\node [left] at (-0.2,0.3) {$\neg$fight};
\node [left] at (-1.1,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {offense};
\node [above] at (2.4,1.4) {defense};
\node [above] at (1.6,1.9) {G (unlimited)};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
\draw[thick,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 2}; % bottom left
\node at (0.8,0.9) {2, 1}; % upper left
\node at (2.4,0.3) {4, 4}; % bottom right
\node at (2.4,0.9) {1, 3}; % upper right
% row player
\node [left] at (-0.2,0.9) {fight};
\node [left] at (-0.2,0.3) {$\neg$fight};
\node [left] at (-1.1,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {offense};
\node [above] at (2.4,1.4) {defense};
\node [above] at (1.6,1.9) {G (limited)};
% Nash equilibrium
\draw[dashed,gray](1.9,0.1)--(2.9,0.1);
\draw[dashed,gray](1.9,0.1)--(1.9,0.5);
\draw[dashed,gray](1.9,0.5)--(2.9,0.5);
\draw[dashed,gray](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:belgium_germany-britain2}
\end{figure}

\chapter{Troubled Partnerships: \\ Coalitions at War}
\chaptermark{Troubled Partnerships}
\label{ch:coalitions}
\bigskip

\begin{figure}
\caption{Coalition Warfare, 1914}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (0,-0.1) {August};
	\draw[thick](0,0.1)--(0,-0.1);
	\node[above] at (0,0.1) {Austria invades Serbia};
	\node[above] at (0,0.4) {Battle of the Frontiers};
\node[below] at (2,-0.1) {September};
	\draw[thick](2,0.1)--(2,-0.1);
	\draw[thick,dotted](2,0.1)--(2,1);
	\node[above] at (2,1) {Ger. troops help Austria};
	\node[above] at (2,1.3) {Battle of the Marne};
\node[below] at (4,-0.1) {October};
	\draw[thick](4,0.1)--(4,-0.1);
	\node[above] at (4,0.1) {Lemberg falls};
\node[below] at (6,-0.1) {December};
	\draw[thick](6,0.1)--(6,-0.1);
	\draw[thick,dotted](6,0.1)--(6,0.75);
	\node[above] at (6,0.75) {Austria expelled from Serbia};
	\node[above] at (6,1.05) {Austria loses Galicia};
\end{tikzpicture}
\end{center}
\label{fig:coalitions_timeline}
\end{figure}

\begin{figure}
\caption{Coalition War Efforts as a Collective Goods Problem}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {4, 1}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {2, 2}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {high};
\node [left] at (-0.2,0.3) {low};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {high};
\node [above] at (2.4,1.4) {low};
\node [above] at (1.6,1.9) {B};
% social optimum
%\draw[thick,blue](0.25,0.6)--(0.25,0.9);
%\draw[thick,blue](0.25,0.6)--(0.75,0.6);
%\draw[thick,blue](0.75,0.6)--(0.75,0.9);
%\draw[thick,blue](0.75,0.9)--(0.25,0.9);
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
\end{tikzpicture}
\end{center}
\label{fig:coalitions_collective_action}
\end{figure}

\begin{figure}
\caption{Private Benefits for Cooperation on the Western Front}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs - imperial competition
%\node at (0.8,0.3) {2, 4}; % bottom left
%\node at (0.8,0.9) {3, 3}; % upper left
%\node at (2.4,0.3) {1, 1}; % bottom right
%\node at (2.4,0.9) {4, 2}; % upper right
% payoffs
\node at (0.8,0.3) {2, 3}; % bottom left
\node at (0.8,0.9) {4, 4}; % upper left
\node at (2.4,0.3) {1, 1}; % bottom right
\node at (2.4,0.9) {3, 2}; % upper right
% row player
\node [left] at (-0.2,0.9) {high};
\node [left] at (-0.2,0.3) {low};
\node [left] at (-1.2,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {high};
\node [above] at (2.4,1.4) {low};
\node [above] at (1.6,1.9) {F};
% Nash equilibrium (the imperial competition equilibrium)
\draw[thick,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:coalitions_selective_incentives}
\end{figure}

\begin{figure}
\caption{Germany Shoulders the Burden on the Eastern Front}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {4, 3}; % bottom left
\node at (0.8,0.9) {3, 4}; % upper left
\node at (2.4,0.3) {2, 1}; % bottom right
\node at (2.4,0.9) {1, 2}; % upper right
% row player
\node [left] at (-0.2,0.9) {high};
\node [left] at (-0.2,0.3) {low};
\node [left] at (-1.2,0.6) {A-H};
% column player
\node [above] at (0.8,1.4) {high};
\node [above] at (2.4,1.4) {low};
\node [above] at (1.6,1.9) {G};
% Nash equilibrium
\draw[thick,gray](0.3,0.1)--(1.3,0.1);
\draw[thick,gray](0.3,0.1)--(0.3,0.5);
\draw[thick,gray](0.3,0.5)--(1.3,0.5);
\draw[thick,gray](1.3,0.1)--(1.3,0.5);
\end{tikzpicture}
\end{center}
\label{fig:coalitions_kgroup}
\end{figure}

\chapter{The Best Laid Plans: \\ Attrition's Static Horror}
\chaptermark{The Best Laid Plans}
\label{ch:attrition}
\bigskip

\begin{figure}
\caption{The Path to Attrition, 1914-1916}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (-1,-0.1) {Aug 1914};
	\draw[thick](-1,0.1)--(-1,-0.1);
	\node[above] at (-.85,0.1) {Battle of the Frontiers};
\node[below] at (1,-0.1) {Sep 1914};
	\draw[thick](1,0.1)--(1,-0.1);
	\draw[thick,dotted](1,0.1)--(1,0.75);
	\node[above] at (1,0.75) {1st Battle of the Marne};
\node[below] at (3,-0.1) {Nov 1914};
	\draw[thick](3,0.1)--(3,-0.1);
	\node[above] at (3,0.1) {1st Battle of Ypres};
\node[below] at (5,-0.1) {May-Jun 1915};
	\draw[thick](5,-0.1)--(5,0.1);
	\draw[thick,dotted](5,0.1)--(5,0.75);
	\node[above] at (5,0.75) {Gorlice-Tarn\'ow Offensive};
\node[below] at (7,-0.1) {Feb-Dec 1916};
	\draw[thick](7,-0.1)--(7,0.1);
	\node[above] at (7,0.1) {Battle of Verdun};
\end{tikzpicture}
\end{center}
\label{fig:attrition_timeline}
\end{figure}

\begin{figure}
\caption{Military Strategies on the Western Front}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {0, 1}; % bottom left
\node at (0.8,0.9) {1, 0}; % upper left
\node at (2.4,0.3) {1, 0}; % bottom right
\node at (2.4,0.9) {0, 1}; % upper right
% row player
\node [left] at (-0.2,0.9) {left};
\node [left] at (-0.2,0.3) {right};
\node [left] at (-1.2,0.6) {F};
% column player
\node [above] at (0.8,1.4) {left};
\node [above] at (2.4,1.4) {right};
\node [above] at (1.6,1.9) {G};
% Nash equilibrium
%\draw[thick,red](0.3,0.7)--(1.3,0.7);
%\draw[thick,red](0.3,1.1)--(1.3,1.1);
%\draw[thick,red](0.3,0.7)--(0.3,1.1);
%\draw[thick,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:attrition_blotto_ad}
\end{figure}

\begin{figure}
\caption{The Grim Logic of Attrition on the Western Front}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 4}; % bottom left
\node at (0.8,0.9) {3, 3}; % upper left
\node at (2.4,0.3) {2, 2}; % bottom right
\node at (2.4,0.9) {4, 1}; % upper right
% row player
\node [left] at (-0.2,0.9) {static};
\node [left] at (-0.2,0.3) {mobile};
\node [left] at (-1.2,0.6) {Entente};
% column player
\node [above] at (0.8,1.4) {static};
\node [above] at (2.4,1.4) {mobile};
\node [above] at (1.6,1.9) {Central};
% Nash equilibrium
\draw[thick,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:attrition_attritionmodel}
\end{figure}

\begin{figure}
\caption{Arming to Change and Defend the Status Quo}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {$0$, $V-b$}; % bottom left
\node at (0.8,0.9) {$-a$, $V-b$}; % upper left
\node at (2.4,0.3) {$0$, $V$}; % bottom right
\node at (2.4,0.9) {$V-a$, $0$}; % upper right
% row player
\node [left] at (-0.2,0.9) {arm};
\node [left] at (-0.2,0.3) {$\neg$arm};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {arm};
\node [above] at (2.4,1.4) {$\neg$arm};
\node [above] at (1.6,1.9) {B};
% Nash equilibrium
%\draw[thick,red](0.3,0.7)--(1.3,0.7);
%\draw[thick,red](0.3,1.1)--(1.3,1.1);
%\draw[thick,red](0.3,0.7)--(0.3,1.1);
%\draw[thick,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:attrition_secrecy}
\end{figure}

\chapter{Choosing Sides: \\ Building Military Coalitions}
\chaptermark{Choosing Sides}
\label{ch:choosing}
\bigskip

\begin{figure}
\caption{Other Powers Fall in Line, 1914-1917}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (0,-0.1) {Sep 1914};
	\draw[thick](0,0.1)--(0,-0.1);
	\node[above] at (0,0.1) {Japan declares war on Ger.};
\node[below] at (2,-0.1) {Oct 1914};
	\draw[thick](2,0.1)--(2,-0.1);
	\draw[thick,dotted](2,0.1)--(2,0.75);
	\node[above] at (2,0.75) {Ottomans join Central Powers};
\node[below] at (4,-0.1) {May 1915};
	\draw[thick](4,0.1)--(4,-0.1);
	\node[above] at (4,0.1) {Italy joins Entente};
\node[below] at (6,-0.1) {August 1917};
	\draw[thick](6,0.1)--(6,-0.1);
	\draw[thick,dotted](6,0.1)--(6,0.75);
	\node[above] at (6,0.75) {China declares war on Ger.};
\end{tikzpicture}
\end{center}
\label{fig:choosing_timeline}
\end{figure}

\begin{figure}
\caption{Italy Chooses Between Rival Coalitions}
\begin{center}
% satiable
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {8, 1}; % bottom left
\node at (0.8,0.9) {2, 3}; % upper left
\node at (2.4,0.3) {4, 2}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {high};
\node [left] at (-0.2,0.3) {low};
\node [left] at (-1,0.6) {Italy};
% column player
\node [above] at (0.8,1.4) {honor};
\node [above] at (2.4,1.4) {default};
\node [above] at (1.6,1.9) {Central Powers};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
%\draw[dashed,red](0.3,0.7)--(1.3,0.7);
%\draw[dashed,red](0.3,1.1)--(1.3,1.1);
%\draw[dashed,red](0.3,0.7)--(0.3,1.1);
%\draw[dashed,red](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
%insatiable
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {3, 1}; % bottom left
\node at (0.8,0.9) {6, 4}; % upper left
\node at (2.4,0.3) {2, 2}; % bottom right
\node at (2.4,0.9) {5, 2}; % upper right
% row player
\node [left] at (-0.2,0.9) {high};
\node [left] at (-0.2,0.3) {low};
\node [left] at (-1,0.6) {Italy};
% column player
\node [above] at (0.8,1.4) {honor};
\node [above] at (2.4,1.4) {default};
\node [above] at (1.6,1.9) {Entente};
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Nash equilibrium
\draw[thick,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,gray](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:choosing_italy}
\end{figure}

\chapter{Coordinating Caution: \\ Naval War in The North Sea}
\chaptermark{Coordinating Caution}
\label{ch:haul}
\bigskip

\begin{figure}
\caption{The War in the North Sea, 1914-1916}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (0,-0.1) {Aug 1914};
	\draw[thick](0,0.1)--(0,-0.1);
	\node[above] at (0,0.1) {Battle of Heligoland Bight};
\node[below] at (2,-0.1) {Nov 1914};
	\draw[thick](2,0.1)--(2,-0.1);
	\draw[thick,dotted](2,0.1)--(2,0.75);
	\node[above] at (2,0.75) {UK blockades Germany};
\node[below] at (4,-0.1) {Jan 1915};
	\draw[thick](4,0.1)--(4,-0.1);
	\node[above] at (4,0.1) {Battle of Dogger Bank};
\node[below] at (6,-0.1) {May 1916};
	\draw[thick](6,0.1)--(6,-0.1);
	\draw[thick,dotted](6,0.1)--(6,0.75);
	\node[above] at (6,0.75) {Battle of Jutland-Skaggerak};
\end{tikzpicture}
\end{center}
\label{fig:haul_timeline}
\end{figure}

\begin{figure}
\caption{Naval Strategy in the North Sea}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 3}; % bottom left
\node at (0.8,0.9) {2, 2}; % upper left
\node at (2.4,0.3) {4, 4}; % bottom right
\node at (2.4,0.9) {3, 1}; % upper right
% row player
\node [left] at (-0.2,0.9) {total};
\node [left] at (-0.2,0.3) {limited};
\node [left] at (-1.2,0.6) {UK};
% column player
\node [above] at (0.8,1.4) {total};
\node [above] at (2.4,1.4) {limited};
\node [above] at (1.6,1.9) {G};
% Nash equilibrium 1
\draw[thick,dashed,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,dashed,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,dashed,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,dashed,gray](1.3,0.7)--(1.3,1.1);
% Nash equilibrium 2
\draw[thick,dashed,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,dashed,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,dashed,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,dashed,gray](2.9,0.1)--(2.9,0.5);
\end{tikzpicture}
\end{center}
\label{fig:haul_navalwar}
\end{figure}

\begin{figure}
\caption{The Sidewalk Problem}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {0, 0}; % bottom left
\node at (0.8,0.9) {1, 1}; % upper left
\node at (2.4,0.3) {1, 1}; % bottom right
\node at (2.4,0.9) {0, 0}; % upper right
% row player
\node [left] at (-0.2,0.9) {left};
\node [left] at (-0.2,0.3) {right};
\node [left] at (-1.2,0.6) {1};
% column player
\node [above] at (0.8,1.4) {left};
\node [above] at (2.4,1.4) {right};
\node [above] at (1.6,1.9) {2};
% Nash equilibrium 1
\draw[thick,dashed,gray](0.3,0.7)--(1.3,0.7);
\draw[thick,dashed,gray](0.3,1.1)--(1.3,1.1);
\draw[thick,dashed,gray](0.3,0.7)--(0.3,1.1);
\draw[thick,dashed,gray](1.3,0.7)--(1.3,1.1);
% Nash equilibrium 2
\draw[thick,dashed,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,dashed,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,dashed,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,dashed,gray](2.9,0.1)--(2.9,0.5);
\end{tikzpicture}
\end{center}
\label{fig:haul_sidewalk}
\end{figure}

\begin{figure}
\caption{The Coordination Problem in Bargaining}
\begin{center}
\begin{tikzpicture}[scale=1.5]
\draw[thick, -](-3.5,0)--(3.5,0);
	\draw[thick](-3.5,0.05)--(-3.5,-0.05);
	\draw[thick](3.5,0.05)--(3.5,-0.05);
		\node [below] at (-3.5,-0.05) {\small{C}};
		\node [below] at (3.5,-0.05) {\small{D}};
	\draw[thick](0.5,0.05)--(0.5,-0.05);
		\node [below] at (0.5,-0.05) {\small{$\wedge$}};
		\node [above] at (0.35,0.05) {\small{focal border}};
	\draw[thick](-1.25,0.05)--(-1.25,-0.05);
		\node [below] at (-1.25,-0.05) {\small{$w_C$}};
	\draw[thick](1.25,0.05)--(1.25,-0.05);
		\node [below] at (1.25,-0.05) {\small{$w_D$}};
	\draw[thick, decoration={brace},decorate](-1.25,1)--(1.25,1);
		\node [above] at (0,1.05) {\small{self-enforcing borders}};
		\draw[thick, dotted](-1.25,0.05)--(-1.25,1);
		\draw[thick, dotted](1.25,0.05)--(1.25,1);
	\draw[thick, decoration={brace,mirror},decorate](-3.5,-0.5)--(-1.25,-0.5);
		\node [below] at (-2.375,-0.5) {\small{$C$'s war payoff}};
	\draw[thick, decoration={brace,mirror},decorate](1.25,-0.5)--(3.5,-0.5);
		\node [below] at (2.375,-0.5) {\small{$D$'s war payoff}};
\end{tikzpicture}
\end{center}
\label{fig:haul_borders}
\end{figure}

\chapter{The Theory of War III: \\ Commitment and War Termination}
\chaptermark{The Theory of War III}
\label{ch:war3}
\bigskip

\begin{figure}
\caption{Extorting a dollar with a hand grenade}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,-1.2)--(0,1.2);
\draw[thick](3.2,-1.2)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](0,-0.6)--(3.2,-0.6);
\draw[thick](0,-1.2)--(3.2,-1.2);
\draw[thick](1.6,-1.2)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {-3, -3};
\node at (0.8,0.9) {1, 0}; 
\node at (2.4,0.3) {0, 1}; 
\node at (2.4,0.9) {0, 1}; 
\node at (0.8,-0.3) {1, 0}; 
\node at (0.8,-0.9) {-3, -3}; 
\node at (2.4,-0.3) {-3, -3}; 
\node at (2.4,-0.9) {-3, -3};
% row player
\node [left] at (-0.2,0.9) {never};
\node [left] at (-0.2,0.3) {if yes};
\node [left] at (-0.2,-0.3) {if no};
\node [left] at (-0.2,-0.9) {always};
\node [left] at (-1.2,0) {me};
% column player
\node [above] at (0.8,1.4) {yes};
\node [above] at (2.4,1.4) {no};
\node [above] at (1.6,1.9) {you};
% Nash equilibrium
\draw[thick,gray](0.3,-0.1)--(1.3,-0.1);
\draw[thick,gray](1.3,-0.1)--(1.3,-0.5);
\draw[thick,gray](0.3,-0.5)--(1.3,-0.5);
\draw[thick,gray](0.3,-0.1)--(0.3,-0.5);
% Nash equilibrium
%\draw[thick,red](1.9,0.1)--(2.9,0.1);
%\draw[thick,red](1.9,0.1)--(1.9,0.5);
%\draw[thick,red](1.9,0.5)--(2.9,0.5);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Social optimum
\draw[thick,gray](1.9,0.7)--(2.9,0.7);
\draw[thick,gray](1.9,1.1)--(2.9,1.1);
\draw[thick,gray](1.9,0.7)--(1.9,1.1);
\draw[thick,gray](2.9,0.7)--(2.9,1.1);
\end{tikzpicture}
\end{center}
\label{fig:war3_grenade}
\end{figure}

\begin{figure}
\caption{Extorting a dollar with a hand grenade (in the extensive form)}	
\begin{center}
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {you};
\draw[thick, ->](0,0)--(1,-1);
\draw[thick, ->](0,0)--(-1,-1);
	\node at (-0.75,-0.4) {\small{no}};
	\node at (0.75,-0.4) {\small{yes}};
	\node at (-1,-1.2) {me};
\draw[thick, ->](-1,-1.4)--(-1.5,-2.4);
\draw[thick, ->](-1,-1.4)--(-0.5,-2.4);
	\node at (-1.5,-1.8) {\small{$\neg\text{d}$}};
	\node at (-0.55,-1.8) {\small{$\text{d}$}};
	\node at (-1.5,-2.6) {\small{$(1,0)$}};
	\node at (-0.5,-2.6) {\small{$(-3,-3)$}};
	\node at (1,-1.2) {me};
\draw[thick, ->](1,-1.4)--(1.5,-2.4);
\draw[thick, ->](1,-1.4)--(0.5,-2.4);
	\node at (0.5,-1.8) {\small{$\neg\text{d}$}};
	\node at (1.45,-1.8) {\small{$\text{d}$}};
	\node at (0.5,-2.6) {\small{$(0,1)$}};
	\node at (1.5,-2.6) {\small{$(-3,-3)$}};
\end{tikzpicture}
\end{center}
\label{fig:war3_grenadeext}
\end{figure}

\begin{figure}
\caption{Backward induction in the dollar-grenade game}	
\begin{center}
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {you};
\draw[thick, ->](0,0)--(1,-1);
\draw[ultra thick, ->](0,0)--(-1,-1);
	\node at (-0.75,-0.4) {\small{no}};
	\node at (0.75,-0.4) {\small{yes}};
	\node at (-1,-1.2) {me};
\draw[ultra thick, ->](-1,-1.4)--(-1.5,-2.4);
\draw[thick, ->](-1,-1.4)--(-0.5,-2.4);
	\node at (-1.5,-1.8) {\small{$\neg\text{d}$}};
	\node at (-0.55,-1.8) {\small{$\text{d}$}};
	\node at (-1.5,-2.6) {\small{$(1,0)$}};
	\node at (-0.5,-2.6) {\small{$(-3,-3)$}};
	\node at (1,-1.2) {me};
\draw[thick, ->](1,-1.4)--(1.5,-2.4);
\draw[ultra thick, ->](1,-1.4)--(0.5,-2.4);
	\node at (0.5,-1.8) {\small{$\neg\text{d}$}};
	\node at (1.45,-1.8) {\small{$\text{d}$}};
	\node at (0.5,-2.6) {\small{$(0,1)$}};
	\node at (1.5,-2.6) {\small{$(-3,-3)$}};
\end{tikzpicture}
\end{center}
\label{fig:war3_grenadespe}
\end{figure}

\begin{figure}
\caption{Incredible commitments and preventive war}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {2, 2}; % bottom left
\node at (0.8,0.9) {4, 3}; % upper left
\node at (2.4,0.3) {3, 2}; % bottom right
\node at (2.4,0.9) {1, 4}; % upper right
% row player
\node [left] at (-0.2,0.9) {pass};
\node [left] at (-0.2,0.3) {attack};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {honor};
\node [above] at (2.4,1.4) {renege};
\node [above] at (1.6,1.9) {B};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Social optimum
\draw[thick,dashed](0.3,0.7)--(1.3,0.7);
\draw[thick,dashed](0.3,1.1)--(1.3,1.1);
\draw[thick,dashed](0.3,0.7)--(0.3,1.1);
\draw[thick,dashed](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:war3_preventive}
\end{figure}

\begin{figure}
\caption{Crisis bargaining and shifting power at $t=1$}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {3, 1}; % bottom left
\node at (0.8,0.9) {4, 2}; % upper left
\node at (2.4,0.3) {3, 1}; % bottom right
\node at (2.4,0.9) {3, 1}; % upper right
% row player
\node [left] at (-0.2,0.9) {honor$_1$};
\node [left] at (-0.2,0.3) {renege$_1$};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {honor$_1$};
\node [above] at (2.4,1.4) {renege$_1$};
\node [above] at (1.6,1.9) {B};
% bottom label
\node at (1.6,-0.5) {original distribution of power, $t=1$};
% Nash equilibrium
\draw[thick,gray](0.3,0.1)--(1.3,0.1);
\draw[thick,gray](0.3,0.5)--(1.3,0.5);
\draw[thick,gray](0.3,0.1)--(0.3,0.5);
\draw[thick,gray](1.3,0.1)--(1.3,0.5);
% Social optimum
%\draw[thick,blue,dashed](0.3,0.7)--(1.3,0.7);
%\draw[thick,blue,dashed](0.3,1.1)--(1.3,1.1);
%\draw[thick,blue,dashed](0.3,0.7)--(0.3,1.1);
%\draw[thick,blue,dashed](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:war3_cpt1}
\end{figure}

\begin{figure}
\caption{Crisis bargaining at $t=2$ after shifted and preserved power}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {1, 3}; % bottom left
\node at (0.8,0.9) {4, 2}; % upper left
\node at (2.4,0.3) {1, 3}; % bottom right
\node at (2.4,0.9) {1, 3}; % upper right
% row player
\node [left] at (-0.2,0.9) {honor$_2^h$};
\node [left] at (-0.2,0.3) {renege$_2^h$};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {honor$_2^h$};
\node [above] at (2.4,1.4) {renege$_2^h$};
\node [above] at (1.6,1.9) {B};
% bottom label
\node at (1.6,-0.5) {$t=2$ if peace at $t=1$};
% Nash equilibrium
\draw[thick,gray](1.9,0.1)--(2.9,0.1);
\draw[thick,gray](1.9,0.1)--(1.9,0.5);
\draw[thick,gray](1.9,0.5)--(2.9,0.5);
\draw[thick,gray](2.9,0.1)--(2.9,0.5);
% Social optimum
%\draw[thick,blue,dashed](0.3,0.7)--(1.3,0.7);
%\draw[thick,blue,dashed](0.3,1.1)--(1.3,1.1);
%\draw[thick,blue,dashed](0.3,0.7)--(0.3,1.1);
%\draw[thick,blue,dashed](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\begin{tikzpicture}[scale=1.5]
% box
\draw[thick](0,0)--(3.2,0);
\draw[thick](0,0)--(0,1.2);
\draw[thick](3.2,0)--(3.2,1.2);
\draw[thick](0,1.2)--(3.2,1.2);
\draw[thick](0,0.6)--(3.2,0.6);
\draw[thick](1.6,0)--(1.6,1.2);
% payoffs
\node at (0.8,0.3) {2, 0}; % bottom left
\node at (0.8,0.9) {3, 1}; % upper left
\node at (2.4,0.3) {2, 0}; % bottom right
\node at (2.4,0.9) {2, 0}; % upper right
% row player
\node [left] at (-0.2,0.9) {honor$_2^w$};
\node [left] at (-0.2,0.3) {renege$_2^w$};
\node [left] at (-1.2,0.6) {A};
% column player
\node [above] at (0.8,1.4) {honor$_2^w$};
\node [above] at (2.4,1.4) {renege$_2^w$};
\node [above] at (1.6,1.9) {B};
% bottom label
\node at (1.6,-0.5) {$t=2$ if war at $t=1$};
% Nash equilibrium
\draw[thick,dashed](0.3,0.7)--(1.3,0.7);
\draw[thick,dashed](0.3,1.1)--(1.3,1.1);
\draw[thick,dashed](0.3,0.7)--(0.3,1.1);
\draw[thick,dashed](1.3,0.7)--(1.3,1.1);
%\draw[thick,red](2.9,0.1)--(2.9,0.5);
% Social optimum
%\draw[thick,blue,dashed](0.3,0.7)--(1.3,0.7);
%\draw[thick,blue,dashed](0.3,1.1)--(1.3,1.1);
%\draw[thick,blue,dashed](0.3,0.7)--(0.3,1.1);
%\draw[thick,blue,dashed](1.3,0.7)--(1.3,1.1);
\end{tikzpicture}
\end{center}
\label{fig:war3_cpt2}
\end{figure}

\begin{figure}
\caption{Commitment and War in the Extensive Form}
\begin{center}
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {A};
\draw[thick, ->](0,0)--(1,-1);
\draw[thick, ->](0,0)--(-1,-1);
	\node [left] at (-0.7,-0.4) {\small{attack}};
	\node [right] at (0.7,-0.4) {\small{pass}};
	\node [below] at (-1,-1) {\small{$(3,2)$}};
	\node at (1,-1.2) {B};
\draw[thick, ->](1,-1.4)--(2,-2.4);
\draw[thick, ->](1,-1.4)--(0,-2.4);
	\node [left] at (0.3,-1.8) {\small{honor}};
	\node [right] at (1.7,-1.8) {\small{renege}};
	\node [below] at (0,-2.4) {\small{$(4, 3)$}};
	\node [below] at (2,-2.4) {\small{$(2, 4)$}};
\end{tikzpicture}
\end{center}
\label{fig:war3_extensive}
\end{figure}

\begin{figure}
\caption{Trade and the Opportunity Costs of War}
\begin{center}
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {A};
\draw[thick, ->](0,0)--(1,-1);
\draw[thick, ->](0,0)--(-1,-1);
	\node [left] at (-0.7,-0.4) {\small{attack}};
	\node [right] at (0.7,-0.4) {\small{pass}};
	\node [below] at (-1,-1) {\small{$(3-d,2-d)$}};
	\node at (1,-1.2) {B};
\draw[thick, ->](1,-1.4)--(2,-2.4);
\draw[thick, ->](1,-1.4)--(0,-2.4);
	\node [left] at (0.3,-1.8) {\small{honor}};
	\node [right] at (1.7,-1.8) {\small{renege}};
	\node [below] at (0,-2.4) {\small{$(4, 3)$}};
	\node [below] at (2,-2.4) {\small{$(2, 4)$}};
\end{tikzpicture}
\end{center}
\label{fig:war3_trade}
\end{figure}

\chapter{The Theory of War IV: \\ Information and War Termination}
\chaptermark{The Theory of War IV}
\label{ch:war4}
\bigskip

\begin{figure}
\caption{Ambushing a professor who just wants to get to happy hour}
\begin{center}
\begin{tikzpicture}[scale=1.5]
	\node at (4,0.2) {me};
\draw[thick, ->](4,0)--(2.5,0);
\draw[thick, ->](4,0)--(5,-1);
\draw[thick, ->](4,0)--(3,-1);
	\node [left] at (3.5,-0.4) {\small{small}};
	\node [right] at (4.5,-0.4) {\small{big}};
	\node at (3.25,0.2) {\small{stay}};
	\node at (2.2,0) {\small{$(0,5)$}};
	\node at (3,-1.2) {you};
\draw[thick, ->](3,-1.4)--(2.5,-2.4);
\draw[thick, ->](3,-1.4)--(3.5,-2.4);
	\node [left] at (2.75,-1.8) {\small{na}};
	\node [right] at (3.25,-1.8) {\small{a}};
	\node at (2.5,-2.6) {\small{$(5,0)$}};
	\node at (3.5,-2.6) {\small{$(-3,-2)$}};
	\node at (5,-1.2) {you};
\draw[thick, ->](5,-1.4)--(5.5,-2.4);
\draw[thick, ->](5,-1.4)--(4.5,-2.4);
	\node [left] at (4.75,-1.8) {\small{na}};
	\node [right] at (5.25,-1.8) {\small{a}};
	\node at (4.5,-2.6) {\small{$(5,0)$}};
	\node at (5.5,-2.6) {\small{$(-1,-5)$}};
\draw[thick, dotted](3.3,-1.2)--(4.7,-1.2);
\end{tikzpicture}
\end{center}
\label{fig:war4_example}
\end{figure}

\begin{figure}
\caption{Information problems and war ($t=1$ and $t=2$ if no prior battle)}
\begin{center}
% resolute
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {A};
\draw[thick, ->](0,0)--(1,-1);
\draw[thick, ->](0,0)--(-1,-1);
	\node [left] at (-0.7,-0.4) {\small{half}};
	\node [right] at (0.7,-0.4) {\small{all}};
	\node at (-1,-1.2) {B};
\draw[thick, ->](-1,-1.4)--(-1.5,-2.4);
\draw[thick, ->](-1,-1.4)--(-0.5,-2.4);
	\node at (-1.5,-1.8) {\small{acc}};
	\node at (-0.55,-1.8) {\small{ref}};
	\node at (-1.5,-2.6) {\small{$(2, 4)$}};
	\node at (-0.5,-2.6) {\small{$(1, 3)$}};
	\node at (1,-1.2) {B};
\draw[thick, ->](1,-1.4)--(1.5,-2.4);
\draw[thick, ->](1,-1.4)--(0.5,-2.4);
	\node at (0.5,-1.8) {\small{acc}};
	\node at (1.45,-1.8) {\small{ref}};
	\node at (0.5,-2.6) {\small{$(4, 2)$}};
	\node at (1.5,-2.6) {\small{$(1, 3)$}};
\node at (0,-3.2) {$\Pr(\text{resolute})=r$};
\end{tikzpicture}
% irresolute
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {A};
\draw[thick, ->](0,0)--(1,-1);
\draw[thick, ->](0,0)--(-1,-1);
	\node [left] at (-0.7,-0.4) {\small{half}};
	\node [right] at (0.7,-0.4) {\small{all}};
	\node at (-1,-1.2) {B};
\draw[thick, ->](-1,-1.4)--(-1.5,-2.4);
\draw[thick, ->](-1,-1.4)--(-0.5,-2.4);
	\node at (-1.5,-1.8) {\small{acc}};
	\node at (-0.55,-1.8) {\small{ref}};
	\node at (-1.5,-2.6) {\small{$(2, 4)$}};
	\node at (-0.5,-2.6) {\small{$(3, 1)$}};
	\node at (1,-1.2) {B};
\draw[thick, ->](1,-1.4)--(1.5,-2.4);
\draw[thick, ->](1,-1.4)--(0.5,-2.4);
	\node at (0.5,-1.8) {\small{acc}};
	\node at (1.45,-1.8) {\small{ref}};
	\node at (0.5,-2.6) {\small{$(4, 2)$}};
	\node at (1.5,-2.6) {\small{$(3, 1)$}};
\node at (0,-3.2) {$\Pr(\text{irresolute})=1-r$};
\end{tikzpicture}
\end{center}
\label{fig:war4_t1}
\end{figure}

\begin{figure}
\caption{Information problems and war ($t=2$ following a battle at $t=1$)}
\begin{center}
% resolute
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {A};
\draw[thick, ->](0,0)--(1,-1);
\draw[thick, ->](0,0)--(-1,-1);
	\node [left] at (-0.7,-0.4) {\small{half}};
	\node [right] at (0.7,-0.4) {\small{all}};
	\node at (-1,-1.2) {B};
\draw[thick, ->](-1,-1.4)--(-1.5,-2.4);
\draw[thick, ->](-1,-1.4)--(-0.5,-2.4);
	\node at (-1.5,-1.8) {\small{acc}};
	\node at (-0.55,-1.8) {\small{ref}};
	\node at (-1.5,-2.6) {\small{$(1, 3)$}};
	\node at (-0.5,-2.6) {\small{$(0, 2)$}};
	\node at (1,-1.2) {B};
\draw[thick, ->](1,-1.4)--(1.5,-2.4);
\draw[thick, ->](1,-1.4)--(0.5,-2.4);
	\node at (0.5,-1.8) {\small{acc}};
	\node at (1.45,-1.8) {\small{ref}};
	\node at (0.5,-2.6) {\small{$(3, 1)$}};
	\node at (1.5,-2.6) {\small{$(0, 2)$}};
\node at (0,-3.2) {$\Pr(\text{resolute})=r$};
\end{tikzpicture}
% irresolute
\begin{tikzpicture}[scale=1.5]
	\node at (0,0.2) {A};
\draw[thick, ->](0,0)--(1,-1);
\draw[thick, ->](0,0)--(-1,-1);
	\node [left] at (-0.7,-0.4) {\small{half}};
	\node [right] at (0.7,-0.4) {\small{all}};
	\node at (-1,-1.2) {B};
\draw[thick, ->](-1,-1.4)--(-1.5,-2.4);
\draw[thick, ->](-1,-1.4)--(-0.5,-2.4);
	\node at (-1.5,-1.8) {\small{acc}};
	\node at (-0.55,-1.8) {\small{ref}};
	\node at (-1.5,-2.6) {\small{$(1, 3)$}};
	\node at (-0.5,-2.6) {\small{$(2, 0)$}};
	\node at (1,-1.2) {B};
\draw[thick, ->](1,-1.4)--(1.5,-2.4);
\draw[thick, ->](1,-1.4)--(0.5,-2.4);
	\node at (0.5,-1.8) {\small{acc}};
	\node at (1.45,-1.8) {\small{ref}};
	\node at (0.5,-2.6) {\small{$(3, 1)$}};
	\node at (1.5,-2.6) {\small{$(2, 0)$}};
\node at (0,-3.2) {$\Pr(\text{irresolute})=1-r$};
\end{tikzpicture}
\end{center}
\label{fig:war4_t2}
\end{figure}

\begin{figure}
\caption{Threats and Crisis Communication}
\begin{center}
\begin{tikzpicture}[scale=1.5]
	\node at (0,0) {N};
\draw[thick,->](0,0.2)--(0,1.5);
	\node [left] at (0,0.75) {\small{irresolute}};
	\node [right] at (0,0.75) {\small{$1-r$}};
\draw[thick,->](0,-0.2)--(0,-1.5);
	\node [left] at (0,-0.75) {\small{resolute}};
	\node [right] at (0,-0.75) {\small{$r$}};
	\node at (0,1.7) {A};
\draw[thick,->](-0.2,1.7)--(-2.2,1.7);
\draw[thick,->](0.2,1.7)--(2.2,1.7);
	\node at (-1.2,1.9) {\small{threat}};
	\node at (1.2,1.9) {\small{$\neg$threat}};
		\node at (0,-1.7) {A};
\draw[thick,->](-0.2,-1.7)--(-2.2,-1.7);
\draw[thick,->](0.2,-1.7)--(2.2,-1.7);
	\node at (-1.2,-1.9) {\small{threat}};
	\node at (1.2,-1.9) {\small{$\neg$threat}};
	\node at (-2.4,1.7) {B};
\draw[thick,->](-2.6,1.7)--(-3.6,2.7);
\draw[thick,->](-2.6,1.7)--(-3.6,0.7);
	\node at (-3,2.4) {\small{f}};
	\node at (-3,1.0) {\small{$\neg$f}};
	\node [left] at (-3.6,2.7) {\small{$(0,1)$}};
	\node [left] at (-3.6,0.7) {\small{$(2,0)$}};
	\node at (2.4,1.7) {B};
\draw[thick,->](2.6,1.7)--(3.6,2.7);
\draw[thick,->](2.6,1.7)--(3.6,0.7);
	\node at (3,2.4) {\small{f}};
	\node at (3,1.0) {\small{$\neg$f}};
	\node [right] at (3.6,2.7) {\small{$(1,1)$}};
	\node [right] at (3.6,0.7) {\small{$(3,0)$}};
	\node at (-2.4,-1.7) {B};
\draw[thick,->](-2.6,-1.7)--(-3.6,-2.7);
\draw[thick,->](-2.6,-1.7)--(-3.6,-0.7);
	\node at (-3,-2.4) {\small{$\neg$f}};
	\node at (-3,-1.0) {\small{f}};
	\node [right] at (3.6,-0.7) {\small{$(0,0)$}};
	\node [right] at (3.6,-2.7) {\small{$(2,1)$}};
	\node at (2.4,-1.7) {B};
\draw[thick,->](2.6,-1.7)--(3.6,-2.7);
\draw[thick,->](2.6,-1.7)--(3.6,-0.7);
	\node at (3,-2.4) {\small{$\neg$f}};
	\node at (3,-1.0) {\small{f}};
	\node [left] at (-3.6,-0.7) {\small{$(1,0)$}};
	\node [left] at (-3.6,-2.7) {\small{$(3,1)$}};
\draw[thick,dotted](-2.4,1.5)--(-2.4,-1.5);
\draw[thick,dotted](2.4,1.5)--(2.4,-1.5);
\end{tikzpicture}
\end{center}
\label{fig:war4_beerquiche}
\end{figure}

\chapter{Too Proud to Fight?: \\ U-boats and American Neutrality}
\chaptermark{Too Proud to Fight?}
\label{ch:merica}
\bigskip

\begin{figure}
\caption{The End of American Neutrality, 1917}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (0,-0.1) {22 January};
	\draw[thick](0,0.1)--(0,-0.1);
	\node[above] at (0,0.1) {``Peace without Victory''};
\node[below] at (2,-0.1) {2 February};
	\draw[thick](2,0.1)--(2,-0.1);
	\draw[thick,dotted](2,0.1)--(2,0.75);
	\node[above] at (2,0.75) {Germany expands u-boat war};
\node[below] at (4,-0.1) {28 February};
	\draw[thick](4,0.1)--(4,-0.1);
	\node[above] at (4,0.1) {Zimmermann note revealed};
\node[below] at (6,-0.1) {6 April};
	\draw[thick](6,0.1)--(6,-0.1);
	\draw[thick,dotted](6,0.1)--(6,0.75);
	\node[above] at (6,0.75) {US declares war on Germany};
\end{tikzpicture}
\end{center}
\label{fig:merica_timeline}
\end{figure}

\begin{figure}
\caption{German Strategy and American Intervention}
\begin{center}
% resolute
\begin{tikzpicture}[scale=1.5]
	\node at (-0.2,0) {G};
\draw[thick, ->](0,0)--(1.5,1);
\draw[ultra thick, ->](0,0)--(1.5,-1);
	\node [left] at (0.75,0.75) {\small{unleash}};
	\node [left] at (0.75,-0.75) {\small{restrict}};
	\node at (1.7,1) {A};
\draw[ultra thick, ->](1.9,1)--(3.4,1.75);
\draw[thick, ->](1.9,1)--(3.4,0.25);
	\node [left] at (2.75,1.6) {\small{u\_join}};
	\node [right] at (3.4,1.75) {\small{$(\underline{p}, 1-\underline{p}-c)$}};
	\node [left] at (2.75,0.4) {\small{u\_neutral}};
	\node [right] at (3.4,0.25) {\small{$(1, 0)$}};
\node at (1.7,-1) {A};
\draw[thick, ->](1.9,-1)--(3.4,-0.25);
\draw[ultra thick, ->](1.9,-1)--(3.4,-1.75);
	\node [left] at (2.75,-0.4) {\small{r\_join}};
	\node [right] at (3.4,-0.25) {\small{$(0, 1-c)$}};
	\node [left] at (2.75,-1.6) {\small{r\_neutral}};
	\node [right] at (3.4,-1.75) {\small{$(\overline{p}, 1-\overline{p})$}};
\end{tikzpicture}
\end{center}
\label{fig:merica_game1}
\end{figure}

\begin{figure}
\caption{Entente Borrowing, German Strategy, and American Intervention}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% Entente
	\node at (-2.1,-2) {E};
\draw[ultra thick, ->](-1.9,-2)--(-0.4,0);
\draw[thick, ->](-1.9,-2)--(-0.4,-4);
	\node [left] at (-1.5,-1) {\small{borrow}};
	\node [left] at (-1.5,-3) {\small{$\neg$borrow}};
% upper branch
	\node at (-0.2,0) {G};
\draw[ultra thick, ->](0,0)--(1.5,1);
\draw[thick, ->](0,0)--(1.5,-1);
	\node [left] at (0.75,0.75) {\small{b\_unleash}};
	\node [left] at (0.75,-0.75) {\small{b\_restrict}};
	\node at (1.7,1) {A};
\draw[ultra thick, ->](1.9,1)--(3.4,1.75);
\draw[thick, ->](1.9,1)--(3.4,0.25);
	\node [left] at (2.75,1.6) {\small{bu\_join}};
	\node [right] at (3.4,1.75) {\small{$((1-\underline{p})(1-d), \underline{p}, (1-\underline{p})V-c)$}};
	\node [left] at (2.75,0.4) {\small{bu\_neutral}};
	\node [right] at (3.4,0.25) {\small{$(0-d, 1, 0)$}};
\node at (1.7,-1) {A};
\draw[ultra thick, dashed, ->](1.9,-1)--(3.4,-0.25);
\draw[thick, ->](1.9,-1)--(3.4,-1.75);
	\node [left] at (2.75,-0.4) {\small{br\_join}};
	\node [right] at (3.4,-0.25) {\small{$(1-d, 0, V-c)$}};
	\node [left] at (2.75,-1.6) {\small{br\_neutral}};
	\node [right] at (3.4,-1.75) {\small{$((1-\overline{p})(1-d), \overline{p}, (1-\overline{p})V)$}};
% lower branch
% should just be subtracting 4 from everything vertically...
	\node at (-0.2,-4) {G};
\draw[thick, ->](0,-4)--(1.5,-3);
\draw[ultra thick, dashed, ->](0,-4)--(1.5,-5);
	\node [left] at (0.75,-3.25) {\small{$\neg$b\_unleash}};
	\node [left] at (0.75,-4.75) {\small{$\neg$b\_restrict}};
	\node at (1.7,-3) {A};
\draw[ultra thick, dashed, ->](1.9,-3)--(3.4,-2.25);
\draw[thick, ->](1.9,-3)--(3.4,-3.75);
	\node [left] at (2.75,-2.4) {\small{$\neg$bu\_join}};
	\node [right] at (3.4,-2.25) {\small{$(1-\underline{p}, \underline{p}, 1-\underline{p}-c)$}};
	\node [left] at (2.75,-3.6) {\small{$\neg$bu\_neutral}};
	\node [right] at (3.4,-3.75) {\small{$(0, 1, 0)$}};
\node at (1.7,-5) {A};
\draw[thick, ->](1.9,-5)--(3.4,-4.25);
\draw[ultra thick, dashed, ->](1.9,-5)--(3.4,-5.75);
	\node [left] at (2.75,-4.4) {\small{$\neg$br\_join}};
	\node [right] at (3.4,-4.25) {\small{$(1, 0, 1-c)$}};
	\node [left] at (2.75,-5.6) {\small{$\neg$br\_neutral}};
	\node [right] at (3.4,-5.75) {\small{$(1-\overline{p}, \overline{p}, 1-\overline{p})$}};
\end{tikzpicture}
\end{center}
\label{fig:merica_game2}
\end{figure}

\chapter{The End of the Beginning: \\ Victory, Defeat, and Peace}
\chaptermark{The End of the Beginning}
\label{ch:termination}
\bigskip

\begin{figure}
\caption{Endgame, 1918}
\begin{center}
\begin{tikzpicture}[scale=1.5]
% timeline
\draw[thick](-2.25,0)--(8.25,0);
\node[below] at (-1,-0.1) {Mar 1918};
	\draw[thick](-1,0.1)--(-1,-0.1);
	\draw[thick,dotted](-1,0.1)--(-1,0.75);
	\node[above] at (-1,0.75) {\emph{Kaiserschlacht}};
	\node[above] at (-1,1.05) {Brest-Litovsk};
\node[below] at (1,-0.1) {Jul 1918};
	\draw[thick](1,0.1)--(1,-0.1);
	\node[above] at (1,0.1) {``Hundred Days'' begins};
\node[below] at (3,-0.1) {Sep 1918};
	\draw[thick](3,0.1)--(3,-0.1);
	\draw[thick,dotted](3,0.1)--(3,0.75);
	\node[above] at (3,0.75) {Bulgarian armistice};
\node[below] at (5,-0.1) {Oct 1918};
	\draw[thick](5,-0.1)--(5,0.1);
	\node[above] at (5,0.1) {Ger. requests armistice};
\node[below] at (7,-0.1) {Nov 1918};
	\draw[thick](7,-0.1)--(7,0.1);
	\draw[thick,dotted](7,0.1)--(7,0.75);
	\node[above] at (7,0.75) {Ger., A-H armistices};
	\node[above] at (7,1.05) {German revolution};
\end{tikzpicture}
\end{center}
\label{fig:termination_timeline}
\end{figure}

\begin{figure}
\caption{German Political Institutions and War Termination}
\begin{center}
% resolute
\begin{tikzpicture}[scale=1.5]
% Entente
	\node at (-2.1,-2) {G};
\draw[very thick, ->](-1.9,-2)--(-0.4,0);
\draw[thick, ->](-1.9,-2)--(-0.4,-4);
	\node [left] at (-1.5,-1) {\small{dem}};
	\node [left] at (-1.5,-3) {\small{$\neg$dem}};
% upper branch
	\node at (-0.2,0) {E};
\draw[thick, ->](0,0)--(1.5,1);
\draw[very thick, ->](0,0)--(1.5,-1);
	\node [left] at (0.75,0.75) {\small{d\_fight}};
	\node [left] at (0.75,-0.75) {\small{d\_stop}};
	\node [right] at (1.5,1) {\small{$(1-\overline{p}-c_G, \overline{p}-c_E)$}};
\node at (1.7,-1) {G};
\draw[thick, ->](1.9,-1)--(3.4,-0.25);
\draw[very thick, ->](1.9,-1)--(3.4,-1.75);
	\node [left] at (2.75,-0.4) {\small{d\_renege}};
	\node [right] at (3.4,-0.25) {\small{$(1-\underline{p}-c_G-r, \underline{p}-c_E)$}};
	\node [left] at (2.75,-1.6) {\small{d\_honor}};
	\node [right] at (3.4,-1.75) {\small{$(0, 1)$}};
	\node at (-0.2,-4) {E};
\draw[very thick, dashed, ->](0,-4)--(1.5,-3);
\draw[thick, ->](0,-4)--(1.5,-5);
	\node [left] at (0.75,-3.25) {\small{$\neg$d\_fight}};
	\node [left] at (0.75,-4.75) {\small{$\neg$d\_stop}};
	\node [right] at (1.5,-3) {\small{$(1-\overline{p}-c_G, \overline{p}-c_E)$}};
\node at (1.7,-5) {G};
\draw[very thick, dashed, ->](1.9,-5)--(3.4,-4.25);
\draw[thick, ->](1.9,-5)--(3.4,-5.75);
	\node [left] at (2.75,-4.4) {\small{$\neg$d\_renege}};
	\node [right] at (3.4,-4.25) {\small{$(1-\underline{p}-c_G, \underline{p}-c_E)$}};
	\node [left] at (2.75,-5.6) {\small{$\neg$d\_honor}};
	\node [right] at (3.4,-5.75) {\small{$(0, 1)$}};
\end{tikzpicture}
\end{center}
\label{fig:termination_game1}
\end{figure}


\chapter{Conclusion: \\ History and the Present}
\chaptermark{Conclusion}
\label{ch:conclusion}
\bigskip

No graphics.



\end{document}